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Monthly Notices of the Royal
Astronomical Society
Royal Astronomical Society, NASA Astrophysics Data
System Abstract Service, OCLC FirstSearch ...
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Astron.
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#
MONTHLY NOTICES
OF THE
ROYAL ASTRONOMICAL SOCIETY,
CONTAINING
PAPERS,
ABSTRACTS OF PAPERS,
AND
REPORTS OF THE PROCEEDINGS
THE SOCIETY, ^^JJ,"''*^^ -
FROM NOVEMBER 1865, TO JUNE 1866.
VOL. XXVI.
BEING THE ANNUAL HALF-VOLOME OF THE MEMOIIIS AND PROCEEDINGS
OF THE ROYAL ASTRONOMICAL SOCIETY.
LONDON:
PRINTED BY
STRANGEWAYS & WALDEN, CASTLE STREET, LEICESTER SQUARE.
1866.
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MONTHLY ^^^
OP THE
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVL November lo, 1865. No. i.
Wabben De La Rue, Esq., President, in the Chair.
Alfred Dawson, Esq., The Cedars, Chiswick ;
Charles Stewart, Esq., Akendon House, Alton, Hants, and
L. Bamett Phillips, Esq., 35 Hunter Street, Brunswick
Square,
were balloted for and duly elected Fellows of the Society.
On the Comets of 1677 and 1683 ; i860 ///., 1863 /., and
1863 VL ByM. Hoek.
§ I. In a former paper I attempted to prove that, before
taking their orbits under the influence of the Sun's attractions,
the Comets i860 III, 1863 I., and 1863 VL, formed a system,
that is to say, at short distances from each other they had
initial movements of the same direction and velocity.
That direction is nearly indicated by the straight line unit-
ing the Sun to y Hydri.
At the end of the same paper I promised to extend my
researches on the Comets that appeared before 1 844.
The following table contains all the cases since the year
155$, in which the question may arise about a cometary sys-
tem, in consequence of the successive apparition of comets
whose aphelia approach each other on the sphere. In these
Digiti
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2 M. Hoeky on the Comets of \6-jj and 1683 ;
investigations I have adopted, as a limit of time the interval of
ten years, as a limit of distance the angle of i o^. I confess
that there is something arbitrary in these limits, but I have
preferred in the beginning not to extend them too much. More-
over, I warn my readers that they may perhaps meet in this
table with some combinations in which the distance somewhat
surpasses the 10°, because I have only measured these dis-
tances on the globe, in order to save the time which would be
required for the calculations.
I find:—
Comets.
1672
1677
1683
Direction
of
Motion.
Dir.
Aphelion.
Ret.
Ret.
Long.
o
279-4
286-4
290*8
Lat.
- 69-4 1
- 75*7 I
- 83-0 I
Notes.
A case analogous to that of the comets
of 1845 and 1846. Two retrograde
motions, with one direct one. Pro-
bably the comet of 1677 is a stranger
to a system formed by the two
others.
1689
Ret.
Ret.
90-1
90-8
+ 0-6
\
■6 j
The orbit of the Comet of 1689 is
rather uncertain. I have adopted
the elements of Vogel.
178511.
1790 111.
Ret.
Ret.
67-8 — 52-9
72-5 - 50-7
J813 II.
1822 III.
Ret.
Ret.
38-6 + 24-7
46-2 + 31-3
1818 I.
1818 III.
Dir.
Ret.
273-8
*75"4
+ 8*4
+ 10-5
The orbit of the Comet 1818 I. is
rather uncertain.
1830 I.
1835 I.
Dir.
Ret.
31-8 - 2-1
28*0 + 4-6
1842 II,
185T IV.
Ret.
Dir.
i8i-2 + 56-6
193-1 + 6l*2
1844 II.
1845 II.
1846 VII.
1847 II.
Ret.
Dir.
1845 I. Dir.
1846 V. Ret.
1846 VTII. Dir.
Ret.
Ret.
9*8 + 22-9
1*9 + 21-0
280-5 — 41-6
275-3
281-0
- 55*4
~ 49*5
347*4
In the § J of my former paper I haye
f already indicated that these comets
answer only by couples to the
fixed limit, and that also they do
not answer to the second con-
ditions of having in their orbits a
single point of intersection. Pro-
bably 1846 V. is a stranger to a
system that may have contained the
two other bodies.
340-7 - 28-9
31*7
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i86o ///., 1863 /., awrf 1863 VL
Comets.
Direction
of
Motion.
ApheUon.
Long. Lat.
1854 II.
Ret.
347*7
— 76*2
1858 IV-.
Ret.
129
-76-7
1854 V.
Dir.
345*7
+ 13*5
I86I III.
Ret.
347-3
+ 18*2
1855 I.
Ret.
35-0
+ 281
I86I I.
Dir.
36-6
+ 32*9
1857 III.
Ret.
57*7
- 380
1857 V.
Ret.
53*7
- 42*9
1857 VI.
Ret.
222*9
- 37*7
i860 II.
Dir.
219*2
- 294
i860 III.
Dir.
303*1
" 73*a
1863 I.
Dir.
313-2
- 73*9
1863 VI.
Dir.
3 '3*9
- 76-4
1862 II.
Ret.
119*6
- 3-6
1864 II.
Ret.
J24-2
- 0*9
System the discussion of which is
given in the former paper.
Combination OTerlooked in the for-
mer paper.
The harvest is nothing less than rich. To the ten cases
belonging to the years 1 844-65, the 288 preceding years have
only added seven new ones, of which, moreover, two depend on
orbits that are less well known. We might have foreseen it.
The period 15 56-1764 contains in my calculations only 46
comets; that of 1764-1840 only 72 comets; whilst the same
number, 72, have appeared in the years 1840-65. Therefore
the number of well-observed comets is 0*22 annually in the
first period ; 0*95 in the second ; and 2*9 in the third.
It was an exception when, before 1 700, a comet was dis-
covered whose aphelion distance from the Sun surpassed some-
what unity, whilst in the period 1 840-65 the number of aphe-
lion distances larger than unity is a third of the whole.
On the one hand, thus astronomers have, by means of their
powerful instruments, extended the sphere in which these
bodies are detected and observed ; on the other hand, the hea-
vens have been explored in the last twenty-five years with a
vigilance formerly unknown.
The first-fruit of it has been the discovery of several peri-
odical comets ; a second one is the knowledge of the cometary
systems.
§ 2. Let us return to our table of concordant aphelia.
How can we distinguish between the cases in which there
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4 M, Hoeky on the Comets of 1677 and 1683 ;
are systems and those where there is a fortuitous coincidence ?
One case only in this table allows of a direct investigation.
It is that of the Comets of 1672, 1677, and 1683. First, let
us examine if their orbits have a common point of intersection.
The calculation, with Halley's elements, gives —
Comets.
Intersectlonal Points.
Long. Lat.
1672 and 1677
1672 and 1683
275^5 - 7»-8 \
2369 - 82-4 S
3iS'9 - 78-8 J
Mean Equinox
1677 and 1683
of 1677*0.
and these comets formed thus no system, what we had already
presumed from the divergency of their motions.
But how is it with those of 1677 and 1683, that have both
a retrograde motion ?
We may invoke here a new principle. In my former paper
I have indicated that we had commonly to seek for the focal
star by which the system was sent to usj^ in the vicinity of the
intersectional point, common to the orbits of all the members of
the system. Now, if we presume that two comets have formed
a system before approaching the Sun, we must calculate the
position of the point of intersection of their orbits; and, if this
point coincide with any other known to us as a centre of
cometary emanations, we may almost rest assured that these
comets formed a system, the origin of which is to be found in
the direction of the intersectional point.
It is the case we have here to do with. Let us reduce the
point of intersection of the Comets 1677 and 1683 to the mean
equinox of 1 864*0, and compare it with those belonging to the
cometary systems of i860 and 1863. We obtain —
Points of I
ntersection.
Comets. '
Long,
Lat
1677 and 1683
318^5
- 7l-8 ,
i860 III. and 1863 I.
316*7
-76-5
Mean Equinox
i860 III. and 1863 VI.
312*3
- 757
of 1 864-0.
1863 I. and 1863 VI.
J20*8
- 78-7 J
After this new coincidence I do not hesitate to express my
opinion that in the vicinity of the point
X = 3i9° ^ = -78°-5
there must be some star that has sent in the direction of our
Sun — first, the comets of 1677 and 1683, secondly, those of
i860 and 1863.
§ 3. In order to justify this opinion, let us make our calcu-
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i86o ///., 1863 /., and 1863 VL 5
lation of probabilities. When we consider the coincidence of
two intersectional points within 2^ as a result of chance, its
probability is 0*0003. A priori we had, therefore, to expect
that we should meet with it in a number of 3333 cases, and it
occurs in 20 cases.
Moreover, a phenomenon of so small a probability is found
to be united to another one that we could as little have had the
mathematical expectation of meeting with in the limited num-
ber of cases actually considered. I mean the coincidence, within
a small circle of a radius of 3^, of the aphelia of three comets
that appeared in the course of 3^ years. The probability of
this phenomenon being only 0*00000049, we could expect to
find it once in 2,050,000 cases, and all our comets furnish only
6,600 cases.
I will pass over in silence the mutual intersection of the
same three orbits within a circle of a radius of i°"5, as well as
the limited distance of 2^*5 from the average aphelion to the
average intersectional point.
The opinion is already sufficiently justified that the com-
pound event we are considering depends on a physical cause.
Is the explanation I have given the right one ? Later inves-
tigations on the comets that are to appear will decide it. For
the present I do not see how to arrive at any other conclusion,
and I will proceed to subject the comets of 1677 and 1683 to
another trial.
§ 4. Were their distances from the Sun formerly nearly
equal ?
The formula
< = C (r + a q)^r-q
with its difierential formula
which suppose a parabolical motion, and in which
log C = 8*875232 - 10 gives the time in years,
log C = 1*437812 gives it in days,
give me for the distances expressed in radii of the terrestrial
orbit: —
Distanee from the Sun.
Gregorian Date.
Comet 1677.
Comet 1683
573-86
600
601*97
837-78
500
502*18
1076*54
400
402*43
1286-93
300^
302*89
146468
200
203*59
l602'00
100
105-14
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6 M, Jloek, on the Comets of 1677 and 1683 ;
and there is no objection, therefore, from that side.*
§ 5. Several questions may arise with respect to the facts
I have just proved.
Firstly, there is the point
x=3i9° ^ = - 78^-5
whose spherical co-ordinates referred to the equator are
« = 4»» 3"'5 J = — 72°o
and which was called the point P' in my former paper.
We might ask ourselves if there is any interest in search-
ing for a star of well-defined parallax in that direction. As
for me I expect that such a star will be found at a few degrees
distance from the point P', for generally we may admit that
the stars whence comets come to our Sun are the nearest to us.
It would not even be necessary to look for such a star P around
the point P', for it has already been demonstrated in § 7 of my
former paper that, in order to come from P' to P, we must
follow on the sphere the average orbit of the comets of 1 860
and 1863, and follow it in the direction of the direct move-
ment.f In other terms, and more generally, if we call M the point
* The last table gives an idea of the manner in which the bodies of this
system were separated under the influence of the Sun. Perhaps some of
my readers like to have before them a similar table for the systems of i860
and 1863. It is this —
Distances from the Sun.
egorian Date.
Comet i8'o III.
Comet 1863 I.
Comet 1863
756-97
600
600-42
600*25
102087
500
500-56
500-36
>i59'57
400
400-67
400-55
1470-01
300
300-86
300-80
164778
200
201-15
20I-20
1785-10
100
101-83
102-11
1833-70
50
5276
53-35
185360
20
24*43
25-52
1857-98
10
15-92
17-36
As to both tables I must remark that the distances, calculated in the
supposition of parabolical orbits, are only approximate. In order to obtain
more correct numbers it would be necessary to make investigations about the
excentricity of each of the orbits. As to that point compare § 10.
t I must beg my readers to consider the following part of this paragraph
as an erratum on the latter part of the § 7 of my former paper, that is to say,
on all what follows in the mentioned § 7, the same words **in the direction of
the direct movement.** As soon as I detected the error contained in that part
I wrote to the Astronomical Society, but it appears that my letter only
reached the Society after the printing of my paper.
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1 860 ///., 1 863 /., and 1 863 VL 7
from which the planetary system removes, P' P M is a great
circle on the sphere, and P lies between P and M.
If the point P were discovered we should be able to deduce
the velocity of the proper motion of our Sun, on which alone
depends the distance P P.
In order to elucidate this let us suppose that P P' is found
to be 5*^, and remember that the proper motion of the Sun,
taken in an opposite direction, marks on the sphere the point
X = 76° 4a' ^ = — 62° 57' ... Mean Equinox of i864'o.
which is distant from P'by 33° 50', or, in round numbers, 34°.
Now, if we call V the velocity of the comet on its entrance into
the sphere of attraction of the Sun, v the velocity of the planet-
ary system, we shall have —
V : V = sin 5° : sin 29°,
or
V = o'i8o V;
and V itself being 0*367 yearly for an excentricity = rooi of
orbit of Comet 1 860 III., the result is
V B 0*066 radii of the Earth's orhit yearly.
I confess that this reasoning is only an example of calcula-
tion based on arbitrary suppositions, but it is proper to show
the consequences that may be derived from the knowledge of
the new facts.
§ 6. We might further put the question if the five comets
that were sent to us by this star have left it simultaneously ;
or, if rather we ought to consider them as despatched at two
different times.
It appears difficult to answer that question satisfactorily,
but we are able to make researches on the possibility of the
circumstances supposed by each of these hypotheses.
Let us, in order to make a trial of the first one, admit —
1. That the parallax of the star is i", or its distance
206265 unities.
2. That its attraction becomes imperceptible at a distance
of 6265 unities, so that there remained 200,000 unities
to be traversed by the comets after their having left the
star.
3. That the comets of i860 and 1863 have left it with velo-
* cities that were exactly equal, and of such an amount
that the orbit of the Comet of i860 III. obtains an ex-
centricity of I'OOI.
The equations of hyperbolic movement (Theoria Mot us
Corporum CcBlestium, § 21 and 22),
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8 M. Hoeky on the Comets of 1677 and 1683 ;
^_ cog|(v " ^) _ ar co8«{(v - ^)
COBi(Y + '^) p COB ^ '
ix.(«--)-Iog« = -—
give, for the case of a very large r, the approximate formulas,
%v gin *4 __ 2r
P C08>/' "" *€
or actually,
log ubb 3*134851 / =s 539061 yean.*
, .^ 200C00
average velocity = r- = 0*37 10 yearly.
To control this result, let us calculate also the velocity at
an infinite distance, given by the formula.
V^
in our case 0'OOioo6 daily, or 0*3672 yearly.
In order to allow of the comet's arrival 200 years sooner,
it is sufficient that this velocity be increased by its ^y^^th
part, that is, by 0*000000372 unities daily, or by 0*66 metres
a second.
As to the divergency of the fragments that arrived succes-
sively in 1677 and i860, let us suppose the Sun to move yearly
two unities through space, an estimation that probably is far
too high. That body should have traversed, then, during
these 180 years a distance of 360, which, seen from the star,
represents an arc of 6' sin 34^ or 3'*6.
If, then, the comets of 1677 and i860 were both fragments
of the same body, it would have been sufficient for them to
have left the star's sphere of attraction, removed 11 unities
from each other, in directions diverging 3I minutes of angle,
and with velocities the difference of which amounts to § metre
per second.
In the actual state of our knowledge there is therefore
nothing absurd in admitting the first hypothesis.
* This result has a very great influence on the reasoning contained in
% 5. In an interval of time comparable to such a number of years the Star
with well-defined parallax of which there is question in § 5, may have had
a very considerable proper motion along the sphere, and be removed far from
the point it occupied when the comets started from it. Nevertheless I have
preferred to retain that paragraph such as it was written in July, for the rea-
sons mentioned in the note attached to it.
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i86o IlL, 1863 /., and 1863 VI. 9
As for the second, according to which we should have re-
ceived bodies despatched at different times by a same star, it is
a question of probabilities.
With a velocity such as probably was nearly that of the
Comets of i860 and 1863, the perihelion distance 5^ = 1*3 cor-
responds to such a direction of the initial movement as causes
the body to pass the Sun at a distance of 27. When this latter
number is doubled the perihelion distance becomes 5*2, that is
to say, the comet is no more visible to the inhabitants of the
Earth.
We may, therefore, compare the phenomenon to a firing at
a target of 1 20 unities in diameter, at a distance of 206265,
and in such circumstances that the person who fires is igno-
rant in what direction the target is to be met with. Its dia-
meter corresponding to 2', the probability is only \ sin *6o",
that a second shot will strike the target already hit by the
first. Firing at random we must discharge 47,300,000 shots
in order to have the mathematical expectation i of producing
the phenomenon.
To come back to our star, even if we knew that it scatters
yearly 131,300 comets in space, even then we might a priori
lay an even wager that the phenomenon of twice striking the
solar target, as an effect of chance, will not occur within 1 80
years.
On the other hand, should there exist a physical cause
which compels two successive shots to differ only 3^' in direc-
tion, and, supposing the target to have been already hit, we
might lay i to 10 that it will be struck again by a second shot,
and even i to i as soon as we know the divergency of the shots,
and accordingly the target's motion, to be reduced to a ^th part.
The admission of the second hypothesis includes therefore
the supposition of a very great number of comets being yearly
hurled into space by the star. Is there anything inadmissible
in the number 1 30,000 ? If we suppose around the Sun, as
a common centre, two spheres, whose radii are unity and Niep-
tuners distance, there will be in the larger one a number of
perihelia 27,000 times greater than that in the smaller sphere,
supposing the perihelia to be uniformly distributed through
space. This being so, the smaller sphere contains on an average
2 perihelia yearly, yrhich gives 54,000 comets passing yearly
through their perihelia within a sphere large enough to contain
our planetary system. Let us add, first, that this number is
doubled as soon as we admit that one half of the comets pass
without being discovered ; secondly, that it seems difficult to
reject this uniform repetition of the perihelia, which makes
their number proportional to the volume of the sphere, that is,
to the cube of its radius.
Finally, neither of the two hypotheses leads us to the ad-
mission of anything absurd. It appears, therefore, premature
for the present to give the preference to either of them.
Digiti
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lo M, Hbek, on the Comets of i6yy and 1683 ;
§ 7. Let us consider the two hypotheses from another point
of view.
If the five comets are fragments of one body, they have
been moving towards the San in directions diverging by no
more than 3 J', and which we may, therefore, consider as
parallel to each other. In that case, the five orbits must have
a single intersectional point.
On the contrary, if they have been despatched at different
times, the intersectional point of the Comets 1677 and 1683 may
difier from that belonging to the Comets of 1 860 and 1 863, and,
in that case, a difference between these points of J° or even 1°
would not at all be astonishing, according to the contents of
§ 4 of my former paper.
Let us take the numbers from § 2. We have thus the
intersectional points
of the Comets of 1677 and 1683, long. = 3i8°'5, lat. = — 78°-8
,, 1863 Land 1863 VI. long. = 32o°-8, lat. = — 78°7
two points, whose mutual distance is nearly J°. It is difficult
for the present to decide whether we must consider them as
two distinct points, or whether we must simply attribute the
difference to the lesser certainty of the ancient orbits.
A new computation of these, based on a new and careful
reduction of the observations, with exact calculation of the
planetary attractions, could alone give us the means of decid-
ing.
§ 8. There remains still the Comet 1 860 III., whose orbit
passes at a distance of more than 1^*5 the average intersec-
tional point of the four other orbits. The most simple suppo-
sition is that this comet has undergone some perturbation.
Indeed, I find that, before passing its perihelion, it was near
the planet Mercuryy namely, at a distance of about 0*04. An
approximate calculation, however, shows me that the attrac-
tion of this planet was insufficient to cause such a notable per-
turbation in the position of the orbit's plane, in the course of
the three or four days during which the two bodies were near
each other.
The phenomenon remains, then, unexplained. Has it had
its origin near the Sun, or, long before that time, in space ?
In the latter case, the Comet 1 860 III., on coming within the
attraction of the Sun, must have had a movement the direc-
tion of which was convergent towards the parallel movements
of the comets of 1863. May not the mutual attraction of these
three bodies have exercised some influence of that kind during
the course of several centuries ?
§ 9. It is easy to denote their relative position, when at a
great distance from the Sun.
First, we have for the mutual inclinations of their orbits,
Digiti
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1 860 ///., 1683 /., and 1 863 VL 1 1
O /
Inclination of the Orbit i860 III. on the Orbit 1863I. =32 29
,, ,, i860 III. „ i863VI.= 20 27
„ ,, 1863 I. ,, 1863 VI. = 12 I
Further, for the perpendiculars drawn from the Sun on the
tangents to the orbits (considered as parabolas), the formula
which gives
Perpendicular.
Gregorian Date. Comet i860 III.
Comet 1863 I.
Comet 1863 VI
756-97 13-26
2l-8s
2808
1020-87 12-IO
19-94
25-63
so that we obtain —
•
Mutual Distances.
75697
Date.
iozo*87.
Comets i860 III. and 1863
I.
I2-8I
11-71
Comets i860 III. and 1863
VI.
16-31
14-90
Comets 1863 I. and 1863
VI.
8-10
7-32
If we prefer to consider the orbits as hyperbolas, we should
have to calculate.
' ▼ 1 - €
and, therefore, we must admit —
1 . That the initial movement is the same for all, or that
IS a constant quantity in the three orbits.
2. That the excentricity of the orbit of 1 860 III. has a
certain value.
Let this quantity be again i-ooi, we obtain then for the
perpendiculars,
12-51 2I-IO i7'i3
and for the mutual distances of the comets in space,
12-51 15-86 7-51.
numbers whose proportions do not considerably differ from
the above given, and which, should it still be necessary, could
give a new proof that before approaching the Sun our comets
were near each other in space, moving in equal directions with
equal velocities.
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1 2 M. Hoek, on the Comets of \6jj and 1683, S^c.
Now it follows from these numbers that, if the comets have
in space exercised some mutual attraction, we must in the first
place seek for the effects of it in the Comets of 1863 which
were always the nearest to each other.
No mutual attraction, therefore, explains the deviation of
the orbit i860 III. We might have recourse to the supposi-
tion of some meeting with an unknown body that may have
more exclusively influenced this comet, but it would be ex-
plaining the unknown by the unknown, and that is a way in
which I do not like to venture.
§ 10. There is still another circumstance worthy of being
mentioned, because it may perhaps lead to a distinction between
the two hypotheses of § 6. I mean the distribution of the
aphelia around the intersectional points. If we follow the
orbits in the direction of the motions of the comets, we meet, in
those of 1 860 and 1 863, with the aphelia before reaching the
points of intersection. The contrary is the case vrith those
of 1677 and 1683.
I do not doubt that there is an intimate connection be-
tween the excentricity of each orbit and the position of its
aphelion with reference to that of the point of intersection.
Further, we have a well-known relation between its excentri-
city and the velocity of its initial movement.
But it seems that any conclusion is premature, before a new
computation of the orbits has been made, with an investigation,
for each of them, of the maximum as well as the minimum of
excentricity, that the observations allow of.
§ II. Let us return for a moment to the differential for-
mula of § 4.
Neglecting the small quantity ^, as we may do in com-
parison to large values of r, we obtain.
'" = ^V^'"-
a formula that enables us to deduce the following result : — ^If
we admit that, at a distance of 600 unities from the Sun, the
different members of a cometary system may have outrun each
other by 10 unities, in consequence of a small difference in their
respective velocities, it is possible that three comets, formerly
united in a system, may pass through their perihelia during a
course of 55 years.
A new combination of our whole stock of aphelion-positions
is, therefore, necessary with adequate enlargement of the limit
of time, which has b^n chosen too small in § i .
I intend to make the investigation.
Utrecht, % July, 1865.
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Rev, F, Howletty on the great Sun-spot of October 1 865. 13
On the great Sun-spot of October 1 865.
By the Rev. F. Hewlett.
Many telescopes were, I hope, directed to the remarkable
spot which forms the subject of the diagrams now suspended
before you.*
The features which this spot exhibited during its develop-
ment were, I conceive, of rare interest, whilst the definition
which prevailed at the time was everything that could be
desired.
It was first observed by me on the morning of the 7th Oct.
last, at 7 A.M., and when not more than about 3" from the
Sun's eastern margin {^g. 1). It then appeared about 57" in
length from N. to S. ; but, in consequence of the extreme
effects of foreshortening on the surface of the sphere, only 3"
in breadth from E. to W.
Narrow though the spot, therefore, at this time appeared,
yet the positions of the umbrae within it were distinctly visible,
and distinguishable from the penumbra in directions of lati-
tude, though I was unable to discern clearly between umbra
and penumbra in directions of longitude.
One feature which it struck me as certainly not often to be
seen at such an early stage of a spot's entry on the disk, was
the appearance of two or three luminous patches of faculae
(immediately adjoining the spot on its following side), which
extended completely up to the very margin of the Sun. It is
seldom, I mean, that any difference of luminosity can be per-
ceived in the Solar photosphere, say, within 1 o" to 1 5" from
the limb ; though, where faculas or other inequalities of lumi-
nosity exist, they are visible enough when further removed
from the margin, their utmost apparent brilliancy manifesting
itself, generally, when they are from 20" to 2' from it, or
thereabouts. By 2*» 1 5" p.m. on the same day (Oct. 7th^ the
apparent mean breadth of the spot had attained about 7 , and
the distance from the limb to the centre of the principal (or
western) umbra was 1 3" (fig. 2).
The distinction between umbra and penumbra was now in
all parts discernible ; and I had at this hour more satisfactory
evidence of the shelving nature of. the sides of a Solar spot
than I think ever occurred to me before ; for the penumbra on
- the following or outer side of the umbra was plainly broader
by about 3" than it was on the preceding or inner side, on
which last, in fact, it could not have been much more than i"
in apparent breadth.
So very shallow, however, is the amount always of this
shelving, at least in the penumbral strata, and so seldom,
comparatively, have I enjoyed the opportunity of observing
the entry or departure of a really good-sized spot, furnished at
* These diagrams were eihibited at the Meeting. Ed,
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14 B^' P' Hewlett, on the great Sun-spot of October 1865.
the same time with a neat and really centrally situated umbra,
that it has only been on two or three occasions, during my six
years' experience, that I can fairly assert that I have seen this
difference of fore-shortening at all. And I cannot bat think
that some of the supposed instances of the kind have been
sometimes fallacious, and that the spots under observation
were not really furnished with centrally placed umbrse, and
not therefore proper subjects for so delicate an investigation.
On the morning of Oct. 8tli the spot had attained a length
of about 76" by an apparent breadth of about 16". Its centre
was now about 5 z" from the Sun's limb ; and the penumbra
appeared equally wide on both the preceding and following
sides of the principal umbra, which lay within the southern
portion of the spot (see fig. 3).
My observations, however, for 8th Oct. were rather hur-
ried, and I am somewhat inclined to question whether there
was really such an absence of umbra in the northern portion,
and I should wish my opinion to be checked by that of any
other observer.
My notes and drawings for the 1 oth Oct. are, I trust, as
correct as need reasonably be required, so far as the instrument
at my command is concerned, aided, moreover, by an atmo-
sphere of unusual serenity (fig. 4).
The centre of the spot (which, it will now be seen, was the
leading one of a group) was at 9 a.m. just about 4' from the
limb. The penumbra had a length of about 80" by a breadth
of 50". The umbra, now of a ragged rectangular form, was
situated as nearly as possible in the centre of the spot. It had
a mean length of 27" by a mean breadth of ly". Two long
promontories of different degrees of luminosity extended far
across the chasm. The brighter one, 7" in length (or 3150
miles) from the southern side; the other about 8" (or 3600
miles) from the northern. As Mr. Brodie observed in a brief
notice of this spot to the Times newspaper, the shorter and
brighter promontory afterwards was separated, and moved
away from the penumbra ; and the commencement of this ope-
ration is plainly visible in my drawing for this day. Not only
was the southern promontory the brighter one by far of the two
just described, but nearly the whole of the southern side of the
umbra was bordered by a luminous band of considerably greater
brightness than the penumbral regions immediately adjoining.
At the same time, the darkness of tint of the eastern side of the
umbra itself was far deeper than that of the western, over
which, especially in its north-west angle, floated a feeble
luminous haze.
As may be seen in the drawing, the penumbra itself was
far from possessing one uniform tint ; but, as is often the case,
was considerably varied by specks and bands.
In a note for Oct. i ith I have entered the following state-
ment: — " Too stormy to obtain a drawing this day; but about
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Rev, F. Howlett, on the great Sun-spot of October 1865. 15
noon the remarkably luminous band, which bordered the umbra
on its south-eastern side, had completely detached itself from
the penumbra, and had assumed the appearance of a narrow-
tortuous * bridge,' nearly conformable to the wavy edge of the
same side of the penumbra ; ramifications of feebly luminous
matter extending into the northern portions of the penumbra."
On October 1 2th the great spot had assumed a very dif-
ferent appearance (fig. 5), partly, perhaps, in consequence of
the almost entire absence now of the effects of fore-shortening,
but even yet more in consequence of the umbra having un-
doubtedly extended itself much more in an easterly and
westerly direction. The great leading spot was now 90" in its
most extreme length by 60" in mean width. From the north-
west side of the umbra projected a long, narrow sigmatoid
promontory, somewhat brighter than the adjoining penumbra,
about 7000 miles long and 1000 miles wide. Other broader
and shorter promontories also stretched into the umbra, whilst
a somewhat crescent-shaped and rather less luminous cloud
floated as nearly as possible over its centre ; some very feebly
illuminated matter extending itself in hazy masses 1 0,000 miles
in length over its south-east portions. One or two bright oval
patches, from 2000 to 2500 miles in length, lay imbedded in
the penumbra, where it was of a somewhat darker hue than the
average tint.
By 4 P.M. the sigmatoid promontory had completely de-
tached itself from the penumbra, and had assumed a simple
crescent form, convex towards the west. Indeed, about one-
third of its length at its south-east extremity had disappeared ;
hence its now crescent shape. Meanwhile, one of the broad
southern promont^ories had nearly united itself to one of the
northern ones, curving towards the north-east as it did so. The
edge of the penumbra generally was characterised by indenta-
tions of considerable depth ; but it was still more ragged on
the day following.
This is shown in the drawing for Oct. 1 3th, and is more
especially to be observed along its southern border (fig. 6).
The remaining outlying and following spots of the group were
now arranged after the fashion of a rude triangle, each of
whose sides was about a minute and a half in length.
The group this day had attained its most central position
on the disk; and as regards size, also, had now reached its
utmost dimensions, being about no'' in length by 60" still in
breadth; and, making every allowwice for its oval and also
somewhat irregular contour, must have had a superficial area
of certainly not less than 972,000,000 square miles. The
remaining small spots had a joint area of about 165,000,000
miles ; making a grand total of displacement of the solar pho-
tosphere to the enormous extent of 1,137,000,000 miles square,
or nearly six times that of the whole surface of the earth !
The penumbra on the morning of the 1 3 th was marked by
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i6 Rev, F. Howlett, on the great Sun-spot of October 1865.
a long dark streak in its northern portion, about 40" in length
and only about 2" in breadth, which by noon had become more
dark and distinct, as if about to become a narrow umbral rift;
and other shorter streaks lay in nearly parallel lines with it,
towards the south-east ; whilst another streak from, its north-
west extremity ran at right-angles into the northern side of
the umbra, and was divided across by a small bright patch at
the hour last mentioned ; by which time also a large square
projecting portion of penumbral matter had nearly detached
itself from the main spot towards the south-east.
But the most remarkable feature, perhaps, this day was a
bright, sharply-defined arch of photospheric matter, about
9450 miles long in its total curve, which floated over the
western side of the umbra, and was united at each extremity
to the northern side of the penumbra.
I was now also able, as I thought, to discern four separate
nuclei in different parts of the great elongated umbra, which
feature itself was not less than 26,000 miles in length by
15,000 in breadth; and wherein, towards the south-east, a
large triangular mass of the feebly luminous haze was still
plainly observable. It is, perhaps, possible that the arch above
described was constructed by the union of one of the promon-
tories with the remains of the sigmatoid extension which existed,
as we have seen, on Oct. 1 2th.
By 8 A.M. on Oct. 14th the great spot presented a very
different appearance (fig. 7). The umbra was completely
divided across into two unequal portions by an exceedingly
bright and nearly straight bridge, 9000 miles long and 1000
miles wide, as before, and which seemed to be formed in part,
possibly, out of a modification of the north-west remains of the
arch of the day previous. It lay exactly over the principal
nucleus of the great umbra, and was considerably dilated at its
northern foot. But whether it was that the arch had swung
itself loose at its north-east extremity, and then subsequently
stretched itself out across the whole width of the umbra, or
whether it was an entirely new extension of photospheric
matter, I was unable to determine; but subsequent observations
have led me to suspect rather the former.
The eastern, and as yet the larger portion of the umbra
was now considerably contracted, as regarded its breadth,
whilst at the same time the long narrow rift had become more
decidedly dark and umbral in its character, in many places.
The other streaks which, as we observed above, lay in direc-
tions nearly parallel with the rift on the 1 3th Oct., were now
replaced by others, and which, in direct connexion with it, ran
off from it into the main umbra, at an angle of somewhere
about 45°.
By 2 P.M. a very narrow streak of bright luminous matter
extended itself from the northern extremity of the bridge all
along the southern edge of the rift, — symptoms of which
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Rev, F, Howlett, on the great Sun-spot of October 1 865. 1 7
formation had manifested themselves as early as 9 a.m. The
rift, moreover, was divided by the luminous matter in two or
three places, previously to its gradual closing up, as it after-
wards proved. Equally curious were certain faint but perhaps
not the less important features observable at this time amongst
the small subordinate spots that followed in the wake of the
principal one. These were evidently diminishing in magni-
tude, but in their manner of closing up they seemed to betray
a noteworthy sort of movement amongst themselves, or perhaps
rather, in the first instance, in the photosphere in which they lay
scattered. The largest of these minor spots (which was of the
dimensions of about 20" by 15") had either drifted away from,
or had been left behind by, its principal ; whilst at the same
time a very peculiar sort of trailing arrangement was being
assumed amongst themselves, indicating a kind of gyratory
movement in the photosphere itself. Many of the little spots
had ceased to exhibit any appearance of umbra, but, on the
other hand, they had become united more intimately one with
the other, by means of a wavy and here and there divaricating
thread of peiiumbral specks running through them ; an arrange-
ment this, which may also be distinctly observed in my records,
for instance, of 11 May, 1863, and of 1 Feb. 1864.
On the 1 5th Oct. I was unable to make a detailed drawing
of the group, but I observed distinctly that the great bridge
had again become thoroughly curvilinear in its disposition
(fig. 8), extending also further up towards the western end of
the umbra, and having a total length of a clear 30" or 13,500
miles. Indeed, in its now modified condition, and as being almost
separated, in its new north-eastern portions, from the adjoining
penumbra, it might almost be stated as being even 48", or 21,600
miles long. The rift was also still plainly to be distinguished,
but its more easterly portions had nearly closed up.
On the morning of Oct. i6th the great spot — (or craters,
as these phenomena have been called by M. Chacomac, and
which term, as Mr. Brodie observed to me, would seem to be a
far more appropriate designation for these mighty gulfs in the
solar surface) — presented a truly marvellous and most inter-
esting appearance. The great western bridge was now rent
entirely asunder. Its northerly half, which remained still con-
nected in that direction with the penumbra, had again become
nearly straight^ and terminated abruptly just above the prin-
cipal nucleus of the great umbra; whilst its other portion
appeared actually to have swung itself round, somewhat after
the fashion of a prodigious flying-bridge {pont-volant) ; and,
remaining still attached by its extremity to the penumbra, as
before, had thrown itself into the form of a huge brilliant
loop ; being exactly a counterpart, in fact, of the curious arch
of Oct. 13th; only it now lay on the southern side of the
umbra instead of the northern.
As regarded meanwhile the promontories generally, some
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1 8 Rev. F, ffowlett, on the great Sun-spot of October 1865.
of them (especially the most westerly ones) appeared to be
obeying some powerful cyclonic impulse, the vortex of which
might be assigned probably to the principal nucleus alluded to
above. But if so, the impulse in question seemed to be mani-
festing itself at a lower level than that of the broken luminous
bridge, and also of the loop ; which last feature had, by noon,
this day, very nearly indeed reached to the northern side of
the umbra.
The other promontories seemed mostly to have one general
tendency of direction towards the west ;- and the same causes
which regulated their shapes and bearings may be seen in the
drawings to have for some time past operated conspicuously
upon the disposition of the rest of the penumbral matter as
well. The subordinate or following spots of the group con-
tinued now rapidly to diminish more and more.
Oct. 17th was the last day on which I was enabled to
obtain a view of the group, and that was but a comparatively
transient one (fig. 10). But the principal spot still appeared
about 95" in length by 65" in breadth. The large umbra (as
I suspected would soon be the case) was now completely
divided into two portions by a broad mass of intervening
penumbra, dotted in three or four places by dusky patches,
indicating the region formerly occupied by the central portions
of the one single umbra. At the eastern border of the lately
formed penumbra just mentioned a small luminous loop was
still observable ; and which I rather think was the diminished
representative of the striking feature of the previous day,
though of this I do not feel quite certain.
At 8 A.M. on the morning of Oct. 20th I observed a some-
what conspicuous and condensed mass of faculsB exceedingly
close to the Sun's western limb, and in a latitude which must
have very nearly coincided with that occupied by the notable
group which had just passed off; and of which, indeed, it was,
probably, for the time, the last indications.
On and after Oct. 20th the Sun^s disk continued absolutely
devoid of spots for fourteen days, till 3d Nov., when one,
about 35'Mn length, possessing two umbrsB, and attended by a
fine display of faculae, made its appearance in nearly precisely
the same latitude as that wherein lay the spot which has
formed the subject of my paper this evening; and we have,
therefore, little room for doubting but what it is the same
interesting visitant again come round, and seeking further
acquaintance.
I have two drawings of it, on my ordinary scale of one
inch to thirty seconds ; and in the second of which the faculse
are unusually distinct, and in part, again, coming up absolutely
to the very margin of the disk.
With regard, finally, to the prolonged absence of £^ts
alluded to above, I would observe, in conclusion, that I have
not known the Sun to be totally devoid of spots for the same
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Rev. F. Howhtty on the great Sun-spot of October 1865. 19
number of days (in the aggregate even) during the last six
years ; and about one-third of those previous blank da3rs have
occurred, be it noted, during about the last six months.
Lastly, then, from all the appearances which have been
presented* by this remarkable spot we may clearly again infer
the fallacy of such theories as would attribute a more or less
solid and simply opaque nature to these wonderful phenomena
(especially the darker portions); be it either that of a cloudy
condensation floating above the photosphere, according to some
physicists, or of actual crysti^ization or other form of more
decided solidification lying upon it, according to others.
Or how can we suppose that the brilliant and mobile phe^
nomena exhibited by the constantly shifting loops, bridges,
promontories, and patches of feebly luminous haze can be
rents merely in, or more or less porous portions of, the inspis-
sated matter, discloBing more or less distinctly the subjacent
solar photosphere ? Would not any such rents, if they were
such, prefer to run their course through the less solid portions
of the mass — through the penumbre, for instance, instead of
the umbrae chiefly, or, more strangely still, through the nucleus
even ? But yet, in figs. 5, 6, 7, 8, and 9, it may be observed
how the intensely luminous promontory, loop, or bridge (as the
case may be), cuts completely through the very ntAdeus itself
of the spot : an almost incredible circumstance this, supposing
the spots to be solidifications of matter ; but perfectly recon-
cileable with the Herschelian theory (which, in general, is that
of nearly all English astronomers who have studied carefully
solar phenomena, as well as that of MM. Schwabe, Chacornac,
Secchi, and other able continental observers), which assumes,
in perfect accordance with the ocular evidence afforded also by
the best and most recent methods of scrutinising the solar sur-
face, that the outer portions of l^e solar orb consist of various
strata or envelopes of incandescent liquid or gaseous matter
(and in which, possibly, may float particles of a more decidedly
solid nature) of diflerent degrees of luminosity, the uppermost
being the brightest, and affected by certain most powerful
motive forces, the true nature of which is yet enveloped in
much obscurity, but which would appear to be, at times, partly
cyclonic and perhaps partly also magnetic in their character ;
and, finally, that the so-called spots or craters are undoubtedly
negative (that is, cavernous), and not positive (that is, con-
cretionary), in their character.
The President said, You will agree with me as to the value
of these continuous observations of Mr. Hewlett. Unfortu-
nately, members who do not attend our meetings have not the
opportunity of seeing how very beautiful are the representa-
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ao Mr. Brodiey Observations on the Solar Craters
tions of Sun-spots, for which we are indebted to Mr. Hewlett.
It is onlj bj continuitj in observations that we can hope
to laj the foundation of a theory which will account for all the
phenomena of Solar Physics. And while for the time we may
accept as useful any theory which will embrace certain phe-
nomena^ it should be laid aside as soon as a more compre-
hensive one is propounded. It is very certain that our
business is to multiply accurate observations, and a good result
will follow. One Uiing seems fairly established, namely, that
there are several layers of matters in the photosphere, but the
relative positions of these strata is still an open question. In
a paper now passing through the press by Mr. Stewart, Mr.
Loewy, and myself, I think some light will be thrown on this
disputed point.
Some Observations on the Solar Craters which appeared on
September 28 and October 8, 1865. By H. Brodie, Esq.
On September 28 a very fine crater was observed to be on
the Sun's disk, the length of the umbra being about 9200 miles.
The penumbra was deeply indented at the bottom, where it met
the umbra, and one of the promontories formed by the indenta-
tions of the penumbra projected much further than the rest ;
the end of this one was observed to break off in the shape of a
roundish mass of luminous matter, having a diameter about
equal to the width of the promontory, from which it separated,
this nodule of matter was not visible about half an hour later,
but seemed to have been diffused on the surface of the umbra,
which was covered with a wispy stratum of thin luminous
matter, except at one place about the centre of the umbra,
where it appeared black, forming the so-called nucleus of the
crater. On one side of the umbra a very unusual appearance
was noticed ; the umbra seemed covered with this luminous
matter in the form of what is commonly called mackerel sky,
or " cirro-cumulus," the nodular portions of which became
smaller as they advanced on to the umbra, and at last diffused
into the wispy stratum before mentioned.
September 30. The umbra similar in appearance to that
of the 28th inst., the whole being maculated with luminous
matter, except the nucleus; these spots of luminous matter
being much softened or diffused at their edges. Many nodular
portions of luminous matter had broken off from the toothed
formation of the penumbra, and were drifting towards the
centre of the umbra, but were soon diffused into the thin lumi-
nous stratum covering the umbra generally. Some of these
toothings, or promontories, were 2" of arc long. The penumbra
was apparently deeply furrowed from the top edge, or Sun's
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which appeared on September 28 and October 8, 1865. 21
surface, to the bottom in tolerably straight and continuoas
channels, very similar to deep-water courses seen on the sides
of a mountain. From watching the effect of these changes it
would appear that portions of the photosphere are continually
breaking away and sliding down the sides of the penumbra,
then breaking off into sm^ round portions and drifting on to
the umbra, where they become diffused into a thin luminous
stratum ; and since this stratum does not become more dense,
it must be presumed that this luminous matter forming the
Sun's surface is absorbed by chemical actions as yet unknown
to us.
October 2. On examining the position of the crater to-day
I find that there has been an axial rotation of about 33 J^ since
September 30. This crater disappeared from the Sun's disk
about October 5.
October 8. Found a very large crater coming on to the
Sun's disk, but too close to edge of disk to examine it well.
October 10. On taking some micrometrical measurements
of the crater, and allowing for the foreshortening due to its
position on the Sun's sphere, the true shape of the crater
appears to be tolerably circular, the umbra having a mean
diameter of about 1 5,000 miles and the penumbra having a
mean diameter of about 38,000 miles. There were two long
promontories of luminous matter stretching on to the umbra,
and nearly opposite to each other, one on each side of the
umbra; of these one measured about 3000 miles in length,
the other about 4200 miles in length. Soon afterwards the
end of the shorter promontory broke off and drifted on to the
umbra ; about three hours later the whole of this promontory
had detached itself from the penumbra, and was being dissi*
pated into thin luminous cloudy stratum.
October 1 1 . The definition this morning is finer than I
have yet seen it ; used a positive power of 470, with a Dawes*
solar eye-piece, and got very sharp definition. The prevalence
of passing clouds rendered it impossible to observe continu-
ously. The length of the umbra to-day was about 18,000
miles, the width about 9700 miles. There was an exceed-
ingly long promontory of luminous matter projecting along the
umbra from one end of the crater, and running tolerably
parallel to one of the sides, and not far from the end of this
promontory was another detached mass of luminous matter,
about 4000 miles long. (See sketch No. i.*) This latter mass
had elongated itself with wonderful rapidity during the pre-
ceding 15 minutes, possibly as much as one quarter of its
length. The umbra was covered with the same sort of macu-
lated, or ^' mackerel-sky " formation of thin luminous stratum,
as noticed in the crater of September 28, especially on the
opposite side to that near which the promontories of luminous
* The several sketches referred to were exhibited at the Meeting. Bd.
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22 Mr. BrodiCy Observations on the Solar Craters.
matter were located. The very long promontory seemed to be
drifting towards the edge of the umbra, while the detached
mass was moving away from the edge, and the two masses
being so contiguous seemed to argue the existence of a cyclo-
nic action of the disturbing causes.
About I \ hours later I found that the detached mass had
formed a junction with the long promontory (see sketch No. 2),
and near the end of this now doubly long promontory there
was a curious network sort of formation, consisting of lines of
thin luminous cloudy stratum ; apparently these had formed by
being condensed from the surrounding thin luminous stratum.
The prevalence of passing clouds prevented my watching these
changes.
October 1 2. The shape of the umbra very greatly altered,
its greatest length this morning was nearly 29,000 miles, while
the greatest length of the penumbra was rather more than
50,000 miles. The long promontory of yesterday had entirely
disappeared, but there was one at the opposite end of the crater
shaped something like an S. (See sketch No. 3.) The singular
changes which took place in connexion with this serpentine
promontory are shown in sketches No. 3, 4, 5, and 6. The
intervals of time being indicated, the outline of the umbra
in these last sketches was taken from the image of the crater
being thrown by the telescope upon a board. I noticed at
one time five nodules of luminous matter that had broken off
from the toothings of the penumbra, all in a row drifting
towards the middle of the umbra, these were soon after diffused
into thin cloudy stratum.
October 1 3. The sketch No. 7 shows another change from
No. 6 that was taken yesterday; the bridge in No. 6 being
entirely broken away, and a second umbra is now breaking
through the penumbra.
These observations were made with an equatoreal of 8 1 -in.
aperture and i\\ feet focal length.
Molesey Gorej Vckfieldt Sussejp,
The President desired to make one remark in reference to
Mr. Brodie's paper, that one of his observations confirms those
of many others, namely, that the luminous matter as it floats
across a spot seems to dissolve and disappear.
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Mr. Fletcher, Remarks on the Solar Photosphere, 23
Some Remarks on the Solar Photosphere.
By Isaac Fletcher, Esq.
Since the date of mycommanication to the Society on the pho-
tosphere of the Sun, printed in the June number of the Monthly
NoticeSy I have on very many favourable occasions examined
with every possible care and precaution the visible surface of
the Sun, employing the same optical means, viz., my 9|*inch
refractor, with a Dawes' solar eye-piece and powers from 100
to 550. The result has been a strong confirmation of the
opinion I have long held, that recent telescopic observation has
(with the single exception of Mr. Dawes' remarkable discovery
of the cloudy stratum ) thrown little, if any, additional light on
what Sir William Herschel aptly termed the " Nature of the
Sun." Nor, when we reflect on the circumstances of the case,
is this to be wondered at, for when that distinguished mau
observed the Sun he knew better how to proceed to counteract
the intense heat of the solar focal point, than to contract the
aperture of his telescope, as has been the fashion (until the last
few years) in more modem times. In observing the Sun, Sir
William placed between the small mirror of his Newtonian
reflector and the eye-piece a rectangular vessel with well-
polished and parallel glass plates at opposite side^, through
which the rays were transmitted on their passage to the eye-
piece. By filling this vessel with water, diluted with ink or
other coloured liquid, he was able to reduce the light and heat
of the solar beam to any amount desired before it was received
by the eye, without any contraction of the aperture of the
telescope.
Under date, May 3, 1801, using a solution of ink, he says,
^^ Through this mixture I can observe the Sun in the meri-
dian, for any length of time, without danger to the eye or to
the glasses, with a mirror of nine inches in diameter, and with
the eye-pieces open, as they are used for night observations."
(That is without coloured glasses.) With this apparatus there
can be no doubt he obtained views of the solar surface equal
in every respect to those more recently obtained by means of
Sun prisms or other glass diagonals, and his description of the
various appearances presented to him corresponds exceedingly
well with what I am able to see with my large refractor. I
am referring now to the general surface of the Sun, and not to
the phenomena visible in the penumbras of spots. In Mr.
Dawes' most interesting paper on this subject, read before the
Society, Jan. 8th, 1864, he gives various extracts from Sir W.
Herschel's first paper on the "Nature of the Sun," corro-
borative of this view of the subject ; but in Sir William's
second paper, printed in the same volume of the Phil. Trans.
(1801), there are various observations recorded which seem to
me conclusive as to the fact of his being perfectly familiar
Digiti
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24 Mr, Fletcher^ Remarks on the Solar Photosphere.
with the "granules** which have arrested the attention of
recent observers, and which some have erroneously supposed to
be identical with the *' willow-leaf " structure figured by Mr.
Nasmyth. I append some extracts from the paper I have
alluded to, premising that, beyond all doubt Sir William's
"corrugations'* are the " rice-grains," " shingle-beach," " mi-
nute fragments of porcelain," and "granules" of recent years.
"March i8, 1801. The corrugations all over the Sun are
beautiful and coarse, resembling small nodules joined together
like irregular honeycomb.
" In a multitude of places the corrugations are quite de-
tached, like luminous wisps, or slender tufts, standing upright.
" March 1 9. The corrugations are rich, and may be called
luminous wisps, being much disjointed except at their bottom ;
they are so rich that they partake of the yellowish colour of
the ridges.
" March 21. At equal distances from the limb the corru-
gations are equally coarse all over the disk of the Sun.
" March 3 1 . An opening very near the preceding limb is
surrounded by a shallow, which is bordered by a luminous
ridge all round it. The opening itself is also bordered by an
elevated edge, which is nearly as high as the general surface of
the corrugations ; but not so high as that which borders the
shallow, and stands above the general surface.
" April I. The Sun is now without any openings ; but the
corrugations are very luminous and rich.
" April 2. The Sun is very rich in luminous corrugations,
interspersed with bright nodules towards the south pole.
"April 10. The Sun is full of rich tufted corrugations.
"April 19. The corrugations are extremely rich. The
whole solar surface seems to be studded with nodules.
" April 20. The whole surface of the Sun is rich ; the
corrugations are tufted.
" April 24. The corrugations seem to be closer than they
were yesterday.
" April 29. I viewed the Sun through a mixture of ink
diluted with water, and filtered through paper. It gave an
image as white as snow ; and I saw objects very distinctly,
without darkening glasses.
" The ridges through this composition appear whiter than
the rest of the Sun.
" The tops of the corrugations are whiter than their inden-
tations, instead of approaching to a yellowish cast, as they do
in my former way of seeing through green smoked glasses.
" The corrugations are very small and contracted to-day."
From these observations and others in Sir William Her-
schel's first paper which Mr. Dawes has laid before the Society,
and a reference to his drawings, I think that no reasonable
doubt can remain on the mind of any dispassionate inquirer,
that Sir William's corrugations are identical with the appear-
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Mr, Fletcher f Remarks on the Solar Photosphere. 25
ances which, under various names, have recently attracted so
much attention.
I think it highly probable that from the date of Sir W.
Herschel's observations to within the last few years, the Sun
has rarely been looked at except with apertures contracted to
2 or 2f inches, and, under such conditions, the wonderful ap-
pearances so graphically described by him are not to be
discerned at alJ, as I have ascertained by direct experiment.
According to the observations of Mr. Nasmyth, the entire
photosphere of the Sun is composed of multitudes of lenticular
objects, exceedingly regular in form and dimensions, crossing
and overlaying each other in every possible direction, and the
mottled appearance of the Sun is due to the interstices caused
by such interlacing. My observations taken with, I believe,
one of the finest telescopes in this country, and under excellent
circumstances, not only fail to support Mr. Nasmyth's conclu-
sions, but give direct and strong evidence to the contrary.
My conclusion is entirely in accordance with that of Sir W.
Herschel and Mr. Dawes ; viz., that the " corrugations ** or
"granules" are portions of the general surface of the photosphere
raised high in the outer and non -luminous atmosphere possibly
by the furious escape of empyreal gas from the regions beneath
the photosphere. I have never seen any appearance whatever
indicative of a structure such as is described by Mr. Nasmyth,
except what was evidently caused for the moment only by
atmospheric disturbance. Nevertheless, I think there is evi-
dence that the photosphere does consist of masses of luminous
cloud of some kind, but probably of a substance (so to speak)
much more dense and solid than our terrestrial clouds. This, I
think, is shown by the manner in which the luminous masses
are drawn out and attenuated on the penumbra of the large
spots. Here they generally present (though with occasional
irregularities, as shown in the beautiful drawings of Mr.
De La Rue and Dr. Miiller) a perfectly radial appearance,
such as one might suppose would be occasioned by a downward
rush of the luminous matter on the sudden removal of support
from beneath. In such a case the denser portions of the
luminous matter and the less dense, would probably so arrange
themselves as to produce the beautiful radial appearance in
question, whilst lateral disturbance would give the leafy or
mossy appearance figured by our President and Dr. Miiller.
An apparently fatal objection to the idea of a downward
rush of the luminous matter is the fact which every observer
has noticed, that there is an evident upheaving of the photo-
sphere round the penumbrae of large spots. It seems, there-
fore, more probable that the appearances on the penumbrse are
caused by an upward rush of gaseous matter, a theory which,
I think, will explain the different appearances surrounding the
nuclei of Spots.
After all, it must be confessed that as yet little progress
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26 The Astronomer Royaly Note on an Error of Expression,
has been made towards a solution of the query, '' What is a
Sun?"
Tan^ank Obtervatory, Cumberland, Nov, 6, 1865.
Mr. Stone : I think in some of his latter letters Mr. Dawes
refers to two distinct cloudy strata which he observed on the
the solar photosphere, one of which he designates as having
coarse and the other finer granulations. I am inclined to
think that the coarser of those are identical with the '' corru-
gations" of Herschel. It would appear therefore that Herschel
overlooked some of the appearances since described by Mr.
Dawes, possibly because his attention was attracted by other
phenomena, for example, the dark interstices which he describes
as existing between the brighter portions of the photosphere.
The Astronomer Royal suggested that possibly the defini-
tion of Herschel's telescope was not so good as those of modem
times.
Mr. Brodie : There may be a difference of opinion as to
what Herschel meant by corrugations, he may have meant the
so-called granules ; but there is another very definite feature
with large instruments, namely, mountainous ridges — almost
like faculae over the whole of the Sun's surface ; these up-
heavals leaving valleys 60" or 70" broad. These ridges of
luminous matter are a separate formation from the small granu-
lated appearance of the Sun, and it is possible that Herschers
corrugations are the ridges.
Mr. Stone : I think he refers to these specially under the
term of ridges.
Mr. Fletcher : The coarse granules on the Sun may be seen
with almost any telescope : one of two inches in aperture will
show them distinctly. But it requires a much larger one to
see the finer granules on the Sun's disk.
Mr. Stone : May I ask you whether you tried to estimate
in any way the dimensions of these granules ?
Mn Fletcher : I think from 2" to 3" or 4".
Mr. Stone : They appear to us to be much smaller.
The President : Certainly they are much larger than the
markings which I considered to be Nasmy th's wiUow-leaves.
Note on an Error of Expression in two Memoirs of the AstrO'
nomer Royal, in the Corrections to the Elements of the
Moon's Orbit. By the Astronomer Royal.
In a Memoir published in the xviith volume of the Memoirs
of this Society, page 53,1 have used the expression *^ the
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Mr. Sylvester^ Lamberts Theorem for Elliptic Motion. 27
inclination [of the Moon's Orbit to the Ecliptic], whose as-
sumed value is i8537"*9, is to be diminished by 2 ^^^^ and its
value is therefore to be reduced to i8535"'46.'* And in a
second Memoir, published in the xxixth volume, page 21, the
same form of expression is used, giving i8535"-55 for the
inclination.
The words here used are incorrect, as will be seen on
reference to the Reduction of Greenwich Lunar Observations,
vol. i. page Ixxix., of which these Memoirs are a sequel. The
number i8537"-9 is the coefficient (slightly altered from Da-
moiseau's i8539"*8) of the first term in the development of the
Moon*s latitude in periodic functions of the true argument of
latitude, and is not the inclination. The same remark applies
to the numbers i8535"'46 and i8535"-55.
The small corrections made to the coefficient of the first
term in the development of latitude correspond without sensible
error to the corrections of the assumed inclination.
I am indebted to the careful examination of M. Delaunay,
and to his courteous communication, for the discovery of this
error.
Royal Observatory f Greenwich, 1^65, Oct. 23.
On Lamberts Theorem for Elliptic Motion.
By J. J. Sylvester, Esq., F.R.S.
The original demonstration by Lambert of the celebrated
theorem which bears his name was a geometrical one, see
Monthly Notices, vol. xxii., p. 238, where this demonstration
is reproduced by Mr. Cay ley. Lagrange has given no less
than three distinct demonstrations of the same : one a sort of
verification by aid of trigonometrical formulae, another founded
on a property of integrals, and a third, perhaps the most re-
markable of all, derived from the general expressions for the
time in an orbit described about two centres of force varying
according to the law of nature by supposing one of them to be
situated in the orbit itself, and to become zero. Notwith-
standng this plethora of demonstration, the following direct
algebraical method of proving from the ordinary formulas
for the time of a planet passing from one point to another,
that, when the period is given, the time is a function only of the
sum of the distances of these points from the centre of force, and
of their distance fi:om one another, may be deemed not wholly
undeserving of notice.
Let g, ^' be the distances of the two positions from the Sun,
c their distance from one another, v, v' the true, «, t^'the excen-
tric, m, m' the mean anomalies thereunto corresponding, e the
exccntricity, «>=wi— w', s =g + g', A=i (5*— c*) : then
Digiti
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z8 Mr, Sylvester y Lamherfs Theorem for Elliptic Motion.
^ =si— « ooBtiy f's=i— « cos If', fN->«~enn«, m'sii'— e sin ii',
^ co8 9:»co8 tf — e, ^ sinr— K 1 -e*8m«,
^' cos r'= cos «'— c, ^' sin r'= >/ i - e* Sinn',
c»=^« + ^'a-2^^'co8 (r'-r).
Writing for brevity c, c', jt, « , for cos «, cos «', sin «, sin m',
and to avoid confusion putting also for the moment i c in place
of the original s and c, we have
A = e^' + ^ ^'cos (r'-r) = i + cc' + *#'— 2C (c + O + e*(i—c <?'-»«').
Let J = .) *'', 'y then J is the determinant
-2(c + c')+2€(i+cc'— **')» c'*— Cf' + 2 «*—«'(c*' + c'*); c#'—c'* + 2 «*'-e*(c «' + <?'*)
-c-c'
I— cc
-i + ec'
Denoting this determinant by
A
D
G
B
E
H
C
F
K
we find
(A, B, C) - 2H (D, E, F) + 2 E (G, H, K) - (o,B,- B),
(A, B, C) - 2 K (E, D, F) + 2 F (G, H, H) - (o,- C, C),
so that J =
A,
o.
B, C
B, - B
C, C
= o.
Hence restoring $, c, instead of J, c, it appears that dtf is
a linear function o^ ds and ef v > ^hat is, ^ is a function of « and
Vy or what is the same thing of s and c, independent of e.
If then, when c= i, the corresponding values of g, g', r, r', w,
u' are r, /, ^, ^', ^, ^', we have cos ^ = — i, cos ^ s= — i,
sin ^ = o, sin ^ = o, r — r^ = c, r -f /= 5, whence writing
I — cos ^ = , I ~ cos « = -^,
2 2
we have finally •> = ^ — ^' — sin ^ + sin ^' as was to be
proved.
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Mr, Tebbuttf Observations of Enck£s Comet, 29
Essentially this demonstration is of the same value as the
first of Lagrange's three methods of proof above referred to,
but with the difference that it leads up to and accounts
beforehand for the success of the transformations therein
employed.
. Observations of Enck^s Cometh By John Tebbutt, jun., Esq.
I succeeded in discovering Encke's Comet on the evening of
the 24th June, with the help of a rough calculation founded
on the theoretical elements in No. 1326 of the^^^roTsomi^cAa
Nachrichteny and assuming its perihelion passage to occur on
the ist June. I found it after a short search, but at a consi-
derable distance from its calculated place. It was about two
minutes in diameter, faint, and without the slighest condensa-
tion of light in the centre. Owing to an unfortunate deten-
tion of the mail-steamer, Mr. Farley's Ephemeris did not come
to hand till the 30th June. Notice of the discovery was at
once forwarded to the Sydney Observatory, and Mr, Smalley
succeeded in observing the comet with the 7-inch refractor on
the 28th June, and three following days. Owing to bad wea-
ther and bright moonlight, Mr. Ellery had not seen the comet
up to the 7th instant. It was re-discovered here after the full
moon, with the assistance of the ephemeris, but it was so faint
as to be hardly distinguishable. The two determinations of
position which I send are the best obtained, and may possibly
be of some value. I hope to be more fortunate in the observa-
tion of Biela's comet, an Ephemeris of which is published in
No. 1 507 of the Astronomische Nachrichten,
I have observations of the variations of « Argus extending
from 1854 to the present time, which I will forward at a
future opportunity. Should not this star be designated as
" Variable" in the Nautical Almanac f It is now of the fifth
magnitude.
Ring-Micrometer Observations of Encke's Comet.
1865. Windsor M.T. App. R.A. App. DecL South.
bms hms o/'
Jane 24 6 56 46 7 56 54*8 ^ 4 3^
29 7 5 34 8 35 o'l U 4 16
The first position is the result of two comparisons with
B. A.C. 2660, and the second of three comparisons with B. A.C.
«975-
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30 Mr. ElUry^ Places of Comet /. 1865.
Mean Places of the Stars of Com(>arison for the beginning of the Year,
and Apparent Places for the Times of Obsenration.
B.A..C. 2660
2975
Windtor, New South WaUt, 17 JtUy^ 1865.
HA.
Mean. App.
Decl. Sooth.
Mean. App.
h m B B
7 5» 59-*3 (59-93)
3° 18 46*7 (6o'-7)
8 40 o'oa ( 0*79)
'3 3 15-3 (3ao)
Places of Comet /. 1865 (GrecU Southern Comet\ deduced
from Observations made at the Melbourne ObservcUory,
By R J. Ellery, Esq.
I forward herewith the final places of the Comet I. 186^,
of which 1 sent you a former notice.
We have only just commenced the zone work, having been
much delayed in clearing up all the older observations. Next
month I will endeavour to give the Society an account of the
method adopted in cataloguing.
Mean Time.
Greenwich
H.A.
1^1
N.P.D.
1^1
No. of
Mea^
■urea.
Compariaon
Star.
d h m B
Jan. 23 23 5 41-7
ta m B
21 13 47-07
8*8%9
133 10 12-7
9-8'378
B.A.C.7439
24 22 46 54-7
21 20 19*26
88364
134 19 6*7
98047
Lao. 8822
25 23 14 26-8
21 27 1-62
8*8229
135 22 40-6
98384
Lac. 8838
26 22 53 37*9
21 33 22*92
8*8506
136 19 10'2
9-8017
« 7th Mag.
27 23 29 54
21 39 5292
88273
137 12 48*4
98480
B.A.C.7591
30 22 53 17-9
21 58 17-95
8*8831
139 23 52-5
97755
i^ 8th Mag.
Feb. 1 23 38 51*1
22 10 28*14
8*8580
140 36 7*0
9*8391
Lac. 9084
2 22 55 30-8
22 16 9*47
8*901 1
141 6 39*7
9*7621
Lac. 91 11
3 22 34 56-4
22 21 52*46
8*9176
141 35 8-0
97133
Lac. 9152
4 22 18 35
22 27 32*40
8-9284
142 I 389
9*6666
B.A.C.7862
7 22 26 27*2
22 44 16*36
8-9388
143 10 15-3
96678
Lac. 9280
8 22 25 495
aa 49 4337
8*9444
143 29 35*1
'9*6600
:Grm8
9 22 27 14*8
22 55 6*i6
89458
143 47 35-a
9-6579
Lac. 9335
12 23 30 40-4
23 10 59*64
8*9215
144 33 59*6
9*7850
B.A.C.8148
16 22 49 48*8
23 30 51*31
8*9571
145 19 38*2
9-6848
B.A.C.8179
27 23 31 19-8
21 9*36
8*9503
146 27 52-3
9-7569
m 8thMag.
Mar. I 23 35 37
29 3844
8*9493
146 34 15*9
9*7626
* 8i Mag.
4 22 24 302
41 45*57
8*9813
146 41 25-6
9-5777
Lac. 182
6 23 16 40*2
49 56*43
8-9641
146 45 5*1
9*7202
*7iMag.
16 22 39 30*2
1 27 48*28
8*9802
146 51 59*2
9*6275
BJL.C.5fti
19 22 24 57'9
1 38 32*14
8*9830
146 52 16*1
9-5864
Lac. 512
Until February 9th the observations were made with the
spider-line micrometer ; on February i oth, 1 3th, and 1 7th, two
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Description of Sharp^s Quadrant, 3 1
thick silver wires were used, one coinciding with a meridian,
the other at an angle of 45^ to it. For the remainder of the
observations an ordinary wire-micrometer was used, the wires
being of thick silver, so as to dispense with lamp illumination.
All the comparison stars have been since observed with the
transit circle, most of them three times at least, none less than
twice. The observations have been corrected for refraction.
Melbourne Observatory^ August 25, 1865.
The Astronomer Royal exhibited a Quadrant, the work of
Abraham Sharp, lately received at the Royal Observatory,
Greenwich, and gave the following account of it : —
The first mention of this Quadrant is in Smeaton's paper in
the Philosophical Transactions^ vol. Ixxvi. for 1786, " On the
Graduation of Astronomical Instruments;" a paper which,
though now entirely superseded as to its fundamental methods
by the process introduced by Troughton, is still in many re-
spects worthy the attention of the astronomical-instrument-
maker. Speaking of Sharp, he says (page 7), ** I believe there
is now remaining a quadrant, of 4 or 5 feet radius, framed of
wood, but the limb covered with a brass plate ; the subdivi-
sion being done by diagonals, the lines of which are as finely
cut as those upon the quadrants at Greenwich."
In Hutton's Dictionary^ article "Sharp," this statement
(with many others) is copied from Smeaton.
In the Philosophical Magazine^ vol. xxx. for 1847, Janu-
ary-June, page 25, is a paper by the Rev. N. S. Heineken,
" On Abraham Sharp's Mechanical Productions.*' Numerous
instruments are mentioned, and among them, this Quadrant,
which Mr. Heineken was so fortunate as to secure from a
tinman, who was about to use the material as old brass for the
manufacture of kettles.
In the present autumn, Mr. Heineken liberally offered this
relic to the Royal Observatory, witii the expression of his hope
that it might be preserved there with the care usually given to
instruments of historical interest. The Astronomer Royal had
no difficulty in making this engagement, as far as his personal
control could extend : and the instrument, separated into parts
as was required for the convenience of carriage, was imme-
diately sent from Mr. Heineken's residence at Sidmouth to
Greenwich. Mr. Heineken pointed out that one piece of wood
was wanting ; this has been supplied at the Royal Observatory,
and in this state of comparative completeness the Quadrant was
exhibited to the Society.
The wooden frame of the Quadrant consists of three radial
bars of oak (of which two are at right angles, and the third.
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32 Astronomer Rot/nly Description of Sharps s Quadrant.
supplied at Greenwich, makes angles of 45° with the others), and
two arch-pieces of oak, one of about 50° and the other of about
60°, whose ends meet in the middle of the quadrant, with raor-
tice-and-tenon connexion, but without any double-curb struc-
ture or frame for breaking joint. Upon the three wooden radii
are three iron radii and four other iron braces and connecting
pieces, screwed to the wood by iron screws tapped into the
wood. There is also an iron band (in two pieces, united by an
intermediate piece) surrounding the wooden arch ; and to this
band the brass arch is attached by ten angle-irons. The brass
arch itself is made of very thin sheet-brass; it is 10 inches
broad in the middle and somewhat broader near the ends. It
is composed of four pieces ; two of the unions (near the two
ends of the arch) are of dovetailed or embattled ends, brazed
together (as in the old Greenwich quadrants); the central
union, at 45°, does not appear to be brazed ; the union seems
to be effected by riveting the two parts to an iron plate below.
A hole, corresponding to the centre of the graduated circular
arcs, was discovered in a small piece of brass which is let into
the edge of one of the radial iron bars ; this hole is only about
I inch in diameter ; it does not appear ever to have had any
centre-work on which an index or telescope could turn. (A
small pin is now inserted in it, for convenient lodgment of the
point of a measuring beam-compass.) Upon the sheet of brass
are several graduated circular arcs, one of which is partly cut
away by the form given to the interior edge of the brass sheet;
but the finished graduation is a band i inch broad very near
the exterior edge of the brass sheet ; its inner radius being
about 4^ 1 1*°, and its outer radius about 5*^ o^ . Its graduations
extend at one end about 3^ beyond the quadrant and at the
other end about 14^ beyond the quadrant. Each degree is
divided into twenty parts of 3' each, at the exterior and
interior defining curves of the band ; and the graduation-points
are connected by diagonal lines. Four intermediate circular
arcs divide the breadth of the band into five parts ; so that,
with a radius properly shaped, an arc would by eye be read to
36". The diagonal lines are very well cut, but are not (as
stated by Smeaton) comparable to those on the Greenwich
quadrants.
It is not easy to imagine for what purpose this Quadrant
was made. Some bolt-holes in the wooden radii seem to make
it probable that it has been fixed to a wall. But there is no
appearance that it has ever carried an index or movable
radius. The frame, throughout, is miserably weak, and it
appears very strange that an experienced workman should
have connected such a careful graduation with such a feeble
basis, whatever were the purpose for which it was to be used.
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On the Occultation-diameter of the Moon, 33
Adverting to the occultation-diameter of the Moon as deter-
mined in Mr. Oudeman's papers (a determination which, from
his personal acquaintance with the author, the Astronomer
Royal accepted as worthy of the highest credit), the Astro-
nomer Royal remarked that it was necessary, in comparing
different determinations, to keep in view the number of
observations on which each was based. The Greenwich de-
termination is founded on the comparison of 295 occultation-
diameters with 440 diameters measured by the telescope under
the most favourable circumstances ; greater numbers probably,
in both kinds, than all other observations combined can supply.
He remarked that these large numbers were obtained by uni-
formly acting on the system of examining in each year the
observations which it would be possible to make in the next
year (in the instance of the telescopic semidiameter, a special
calculation being necessary for every day) ; so that, when the
time for observation arrived, every observer and every instru-
ment were in readiness to make the observation.
The President, after tendering the thanks of the Society to
the Astronomer Royal for his valuable communication men-
tioned that the semidiameter of the Moon, which he had been
enabled to calculate from photographic observations of the
/'Qf^Q Total Eclipse of 18/0, coincided with the Astronomer Royal's.
Those which he had selected (without knowing the Astrono-
mer Royal's result) as best representing the observations which
he had made concurred absolutely to the second decimal figure
with those which the Astronomer Royal had selected as the
best, namely, the occultation of a star at the dark limb, and its
reappearance at the dark limb of the Moon. Mr. De La Rue,
in consequence of the success of this experiment, had very
great faith that astronomical photography would give here-
after, in certain classes of observations, very accurate results.
In connexion with this subject he also stated that there had
been a meeting the preceding day of the Lunar Committee of
the British Association, and after much discussion it had been
decided to make use of photographs to prepare an accurate
outline map of the Moon ; and it was intended to distribute
portions of these maps to observers who would kindly lend their
aid towards producing a more accurate representation of our
satellite than existed at present. Following in the same path,
he ventured to solicit amateur astronomers to send him an ac-
count of their optical means of observation, with the possibility
of suggesting a distribution of work. It was proposed that the
Moon should be observed in zones of about a degree in width,
that every observer would have apportioned to him a zone,
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^u-t^/
3 4 Elements of Minor Planet
and whenever the Moon was above the horizon some part of
the zone would be visible.
Those who had followed lunar photography would be
aware that it had its rise in America. Perhaps he (the Pre*
si dent) had, by his experiments and the application of time
and what talent he possessed, wrested the palm from the
Americans ; but it was impossible always to hold the sceptre ;
and he was very glad to be able to say that there were two
contributions, one by Mr. Draper, the son of Dr. Draper — a
name celebrated in photography — and another by Mr. Ruther-
ford, whicl^^surpassed the best which he (the President) had
obtained ; and he recognised this as a mark of progress in
astronomical photography.
The President : I perceive on the table an Ephemeris of
Biela's Comet, and I take this opportunity of stating that,
having had the advantage of this and earlier ephemerides
calculated by Mr. Hind, I have searched diligently, but unsuc-
cessfully, for that comet with my 13 -inch reflector.
Mr. Beck presented to the Society a set of stereoscopic
views of Lunar Eclipses, by combining pictures obtained by
Mr. De 14a Rue of the eclipses of February 1858 and October
1865.
Elements of Minor Planet @ Clio.
The following set of Elements, calculated by Prof. De Gas-
paris from observations of August 25 and September 4, 12, and
12, are given Astron. Nach. No. 1554; —
Epoch, August 25*49830, Greenwich Mean Time.
O #
Long, of Epoch = 331 54 4^ '3]
{T = 338 42 9*4 I- Mean Equinox 15 Sept. 1864.
Q = 327 22 28*9 J
t = 9 23 16-3
loge = 9*372048
logfl = 0*373172
The latitudes for the first and fourth observations, calcu-
lated with the foregoing elements, were
+ o°5'a7"*8 and +4° 21' 28^*5
the observed latitudes being
+o°5'29"*i and +4*2x'3o"*6
Digiti
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Miscellaneous, 35
Discovery and Elements of Minor Planet @.
The Planet was discovered by Dr. C. H. F. Peters, at the
Hamilton College Observatory, Clinton, N. Y., on the 19th
September, being seen as a star of the tenth magnitude. The
following set of elements, calculated by Dr. Peters from ob-
servations of Sept. 20, 25, and 30, are given Astron, Nach.
No. 1554:—
Epoch, 1865, Jan. o, BerHn Mean Time.
Mean Equinox 1865*0
Mo
=
329 8 28*6
a*
=
320 34 33-2
9>
=
204 55 5-2
i
=
9 46 339
^
=s
15 20 i7'o
A*
=
824"- 104
log a
=
0*422683
A number of copies of a paper entitled " Researches on
Solar Physics," by Messrs. De La Rue, Stewart, and Loewy,
have been placed at the disposal of the Fellows of the Astro-
nomical Society. Those gentlemen desirous of receiving a copy
are requested to send their names to the Assistant Secretary.
The President's soiree will be held at Willis's Rooms, on
Wednesday, the 17th of January, 1866, at nine o'clock; for
which cards of invitation are about to be issued. Gentlemen
desirous of contributing objects for exhibition are requested to
communicate to the Assistant- Secretary the nature of the pro-
posed exhibits.
The attention of the Council has been called to an omission
which occurs in their last Annual Report ; the signatures of
the Auditors ought to have been attached to the revenue
account and balances for the year.
The plates containing eight representations of the planet
MarSy to illustrate Mr. Dawes's paper, Vol. XXV., p. 225, will
be issued with the next number of the Monthly Notices.
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36
CONTENTS.
Page
Fellows elected i
On the Comets of 1677 and 1683; i860 III., 1863 I., and 1863 VL,
byM. Hoek ib.
On the great Sun-spot of October 1865, by the Rev. F. Howlett ... 13
Some Observations on the Solar Craters which appeared on September
28 and October 8, 1865, by Mr. Brodie 19
Some Remarks on the Solar Photosphere, by Mr. Fletcher 23
Note on an Error of Expression in two Memoirs of the A&tronomer
Royal, in the Corrections to the Elements of the Moon's Orbit, by
the Astronomer Royal 26
On Lambert's Theorem for Elliptic Motion, by Mr. Sylvester 27
Observations of Encke's Comet, by Mr. Tebbutt 29
Places of Comet 1. (Great Southern Comet), deduced from Observa-
tions made at the Melbourne Observatory, by Mr. Ellery 30
Description of Abraham Sharp's Quadrant, by the Astronomer Royal ... 31
Remarks on the Occultation-diameter of the Moon as determined in Mr.
Oudeman's Papers, by the Astronomer Royal 33
Elements of Minor Planet (g) C?io 34.
Discovery and Elements of Minor Planet (g) ib.
Miscellaneous 35
Printed by Strangbways and Walden, Caatle St. Leicester Sq. and Published
at the Apartments of the Society, Dec. 12, 1865.
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^ University c
MONTHLY NOTICES
OF TUB
ROYAL ASTRONOMICAL SOCIETY.
Vol, XXVL December 8, 1865. No. 2.
Warbbn De La Rub, Esq., President, in the Chair.
Capt. Oliver Haldane Stokes, R.E., Co. Kerry, Ireland ;
Henry Samuel Williams, Esq., Cambridge ; and
William Jardine, Esq., 8 King's Bench Walk, Temple,
were balloted for and duly elected Fellows of the Society.
On the Determination of the Difference of Longitude between
the Observatories of Greenwich and Glasgow by Galvanic
Signals. By Professor Grant, F.R.S.
One of the earliest objects which I had in view after
obtaining the definitive control of this Observatory in May
1 860, was to take steps for effecting a new determination of
the longitude of the Observatory relatively to the Royal
Observatory, Greenwich, by means of some one or other of the
various methods founded upon the transmission of galvanic
signals, which have been used so extensively and with so
much success in recent years both in the new and the old
world.
But an impediment of a serious nature offered itself at the
Digiti
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38 Prof. Grants on the Difference of Longitude between
outset to the execution of anj operation of this kind. The
distance between the Observatory and the nearest telegraph
station in the city of Glasgow was nearly three miles. Conse-
quently, an electric communication could not be established
with Greenwich until this hiatus was traversed by a wire,
and one too which would necessarily have to pass over the roofs
of the houses throughout almost the whole of its course.
Fortunately, the negotiations for supplying the city of Glas*
gow with the Mr^&Astghi of dohrdbt time resulted in the
Observatory obtaining the means of enabling it to overcome
this difficulty. Towards the close of the year 1 863 a metallic
connexion was finally established' between the Observatory
and the office of the British and Irish Magnetic Telegraphic
Company, which possesses the patent right of Jones's method
of regiilsting^ <ilodks, and ykhi6ti hhA siti6e becld ext^slvely
employed in carrying that method into effect in Glasgow in
concert with the Observatory. Shortly afterwards, having
brought before the notice of the Astronomer Royal the de-
sirableness of determining by gtflvanie signals the longitude of
the Glasgow Observatory, Mr. Airy very kindly and liberally
offered to place the resources of the Royal Observatory at our
disposal, with a view to the accomplishment of this object, as
soon as a convenient occasion presented itself for conducting
the operations!
The next step was to obtain from one of the principal
Telegraph Companies the temporary use of a wire from Glas-
gow' to tondori, with the view of establishing an unliro^Lcn
electric communicatiph l^etween the two Observatories. This
was speedily etfecled by ihe good offibes of Mr. F. G. Varley,
the Engineer of the Electric and International Tde^raph
Company, who, happening to be in Glasgow at the time when
the project was beginning to acquire shape, at once entered
warmly into our views, and upon his representations the
Company to which he is attached most obligingly assigned to
us the use of one of their through wires during the whole time
that it would be required for the undertaking.
Thd Ai^tronbttier fioyal haVifi^ kihdiy ddbmitti^d* t6 my
choice* several mod^d of conducting ih^ 6]^ViJtion, i sel^Vited
for that purpose the methbd' of doubti^ rb^^i^a'tion; v^hioh has
be«i practised so successfully in the United States of America
and more recently ii^ Europe. The principle of this method is
extremely simple. , When a star, passes each of the successive
wires of the transit telescope of the more eastern of the two
Observatories, the observer, by tapping a key with his finger,^
completes a galvanic circuit, « and the instant of transit is
recorded on the chronographic apparatus of the Observatory ;
but the galvanic current, instead of going to earth, is made to
pass along the line wire to the recording apparatus of the
distant observatory, upon which also the instant of transit is
in the same way recorded. A process exactly similar is re-
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the Ob^ervaiimes^qf' Grtenwish and^Glasgaw, 39
peated wheq the- star oomes to the meridian of the more
western observatory, the instant of transit being registered on
both chronographic apparatuses by. the same completion of the
galvanic circuit. Iti this manner each signalling star supplies
two pairs of recorded times of transit, a comparison of the
individual values of which give two distinct results, the one
indicating the difference of longitude between the two ob-
servatories, and the other assigning a value of the time oc-
cupied by the galvanic current in its passage from the one
observatory^ to the other.
The batteries and the recording apparatus used at this Ob-
servatory were courteously lent to us for the oceasion by the
Electric and. International Telegraph Company. The insula-
tions continued perfectly satisfactory throughout the whole
period of the operations ; the working of the chronographic
apparatus temporarily used by us was also everything that
could be desired.
In order that we might the more easily understand each
other at the two Observatories, Mr. Varley made arrangements
by which each Observatory was supplied with a speaking clerk
from the Electric and International Telegraph Company on
every night of observation.
The period of operations extended from April 28 in the
present year to May 26.
The stars selected for observation amounted in number to
twenty- eight, and were arranged in four groups of seven stars
each, and in such a manner that when the last star of any group
had passed through the telescope of the Glasgow Transi^Circle,
which was the more western instrument, the first star of the
succeeding group was nearly about to commence its passage over
the wires of the Greenwich or more eastern instrument.
The weather on the whole was not favourable for simulta-
neous observations at both Observatories during the period of
four weeks over which the operations extended. In several
instances observations were made at Greenwich which could
not be responded to from Glasgow, and in one or two instances
the converse of this happened. On four nights, however — May
I, May 2, May 22, and May 25 — the sky was favourable for
observation at both Observatories^ and it is upon the results
obtained on those nights that the determination of the differ-
ence of longitude contained in this paper is exclusively based.
The observers at Greenwich were Mr. Dunkin, Mr. Cris-
wick, and Mr. Carpenter ; the observer at Glasgow was Mr.
PlttBoaer. The observations of Mr. Criswick and Mr. Carpen-
ter have been reduced to those of Mr. Dunkin by taking into
account their relative personal equations, the latest determi-
nations of which have been kindly forwarded to me by the
Astronomer Royal. The observations of Mr. Plummer, whose
personal equation was also determined at Greenwich, have
similarly been reduced to those of Mr. Dunkin.
Digiti
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40 Prof. Grants on the Difference of Longitude between
The following are the results of the operations : —
May I.
star.
B.A.C. 4662 ...
rVirginis
d Bootis
26 Bootis
r Bootis
Lalande 26696
B.A.C. 4846 ...
Lalande 26816
o Bootis
Lalande 26975
Ezeetf of Olugow otot Greenwich
Time of Transit as record .'d on
Greenwich Chronogn^h.
m ■
17 >o'73
10-87
IO*S2
10*81
10*64
10*67
io'73
^o'SS
10*64
10*57
Mean Difference
17 10*703 ... (A)
Star.
Ezaeas of Glasgow over Greenwich
Time of Transit as recorded on
Glasgow Chronograph.
B.A.C. 4662
17 IO-74
r Virginis
10*75
d Bootis
...
10*78
26 BootU ...
...
10*68
r Bootis
10*68
Lalande 26696
10*57
B.A.C. 4846 ...
10*76
Lalande 26816
... ...
IO-49
Bootis
...
10*58
10*55
Mean Difference
17 10*658 ...(AO
ice combining (A) and (A'), we have
Difference of
'Longitude ... 17
8
10*680
Time of Current's Passage ...
0*023
Star.
May 2.
Excess of Glasgow over Greenwich
Time of Transit as recorded on
Greenwich Chronograph.
T Virginis ...
...
ID ■
17 10*77
Lalande 25818
...
io*6»
Lalande 25892
10*73
Lalande 25943
10*63
Digiti
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the Observatories of Greenwich and Glasgow. 41
star.
d Bootis
26 Bootis
r Bootis
Lalande 26696
B.A.C. 4846 ...
Lalande 26816
Bootis
Lalande 26975
Lalande 27718
^ Serpentis ...
40 Serpentis ...
y Serpentis ...
Lalande 29100
5 Hercnlis
45 Serpentis ...
Exceis of Glasgow over Greenwich
Time of Transit, as reoorded on
Greenwich Chronogr^h.
17 io'5»
10*70
10*69
10*72
10*62
10-54
io'6o
10*75
10*70
10*85
10*77
IO-79
10*61
10*72
10*73
Mean Difference
17 10*685 ... (B)
Star.
92 Virginis ...
B.A.C. 4662 ...
T Virginis
Lalande 25818
Lalande 25892
Lalande 25943
d Bootis
26 Bootis
r Bootis
Lalande 26696
B.A.C. 4846 ...
Lalande 26816
Bootis
Lalande 26975
Lalande 27718
^ Serpentis ...
40 Serpentis ...
y Serpentis ...
Lalande 29100
5 Hercnlis ...
45 Serpentis ...
Excess of Glasgow over Greenwich
Time of Transit as recorded on
Glasgow Chronograph.
17 10*56
10*62
xo-74
10*56
10*66
10*51
10*50
10*60
10*61
,10*62
io*59
10*47
io*55
10*70
10*60
10*64
10*66
10*69
10*57
10*66
IO-73
Mean Difference
17 10*611 ... (B')
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42 Prof, Chanty on the Difference of ^Longitude between
Combining (B) and (B'), we have
m 8
Difference of Longitude ... 17 10*648
Time of Current's Passage ... 0*037
May 22.
star.
rBootis
Lalande 26975
.Lalande 27718
3 Serpentis ...
Lalande 27885
£ Serpentis ...
8- Serpentis ...
r Serpentis ...
la Serpentis ...
^ Serpentis ...
7 -Serpentis ...
5 Herculis ...
45 Serpentis ...
ExoesB of Glasgow over Greenwich
Time of Tvaasit as recorded on
Greenwich Chronograph.
17 lO'SS
w-49
10*42
10-58
10-58
10-50
10*42
10-50
io*35
1035
10-46
10-52
10-36
Mean Difference
17 10*468 ... (C)
Star.
Excess of Glasgow over Greenwich
Time of Transit. as recorded on
GUuqpow Ghronograph.
9 Bootis
...
... 17 10-44
Lalande 26975
...
10-40
Lalande 27718
...
10-42
3 Serpentis ...
...
.10-56
Lalande 27885
...
IO-49
6 Serpentis ...
10-42
8 Serpentis ...
...
IO-33
T Serpentis ...
...
10-44
10 Serpentis ...
...
10-27
^ Serpentis ...
...
10-30
y Serpentis ...
10-47
5 Herculis
...
10-36
45 Serpentis ...
...
10*27
Mean Difference
... 17 10*398 ... (C)
ftbining (C) and
(C),
we have
Difference of Longitude
17 IO-433
Time of Cuire&t's
Passage ...
0-035
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ihe.Ojfservatorieso/i^^ei^wiQh and ,Qlf^sgpia. ,43
May 25.
gStar.
26 Bootis
rBootis
iidaiQ^e ;».6696
B.A.C. 4846 ...
Lalande 26816
« Bootis^
Lalande 26975
Lalande 27718
3 Serpentis ...
Lalande 27885
6 Serpentis ...
8 Serpentis ...
T Serpentis ...
10 Serpentis ...
40 Serpentis ...
y Serpentis ...
5 Herculis
L«laode^292j$i
45 Serpentis ...
Excess of Glasgow oTor Greenwich
Time of Transit, as recorded on
Oreen w^(^ Clir9nQ^aph.
^7 10*52
10*31
10*41
10*48
J9\SS
10*48
10*38
io*6i
io'49
10:51
10*42
io'33
IO-57
10*48
10*48
10*48
10*76
'<5-54
10*32
Mean Difference
17 10*480 ... (D)
Star.
26 Bootis
0- Bootis
Lalande 26696
B.A.C. 4846 ...
Lalande 26816
« Bootis
Lalande 26975
Lalande 27718
.3 Serpentjs ...
Lfilande ^7885
, 6.§f|rpeptis ...
iS^^Sprpeptis ...
r Serpentis ...
10 Serpentis ...
40 Serpentis ...
y Serpentis ...
I ^eSxceps of Glasgow orer Greenwich
Time of Transit, as recorded on
Gla^pow Chronograph.
m 8
»7 io'47
IO-35
10*36
10*41
, lO'S2.
1043
io*37
">'57
10*^8
'^!^^
}p*^o
10*31
• 10*52
,^0*50
10*50
10*50
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44 ^of. Grant, on the Difference of Longitude, S^c,
Excess of Glasgow over Greenwich
Star. Time of Transit, as recorded on
Glasgow Chronograph. '
m s
5 Hercolis 17 10*61
Lalande 29261 10*43
45 Serpentifl 10*24
Mean Difference ... 17 10*445 ... (DO
Combining (D) and (D'), we have
m 8
Difference of Longitude ... 17 10*463
Time of Current's Passage ... 0*018
Collecting together the mean values of the difference of
longitude for the four days, we have
May I
2
Difference of liOngltude.
m ■
17 io*68o
io'648
22
IO-433
10*463
Combining these together with a due regard to the number
of observations on each day, we obtain for the definitive value
of the longitude of the Transit Circle of the Glasgow Observa-
tory,
i7» io»-55 W.
Similarly, for the time of the current's passage.
May I
0*023
2
0*037
22
0*035
»5
0*018
Whence we obtain definitively
Time of Current's Passage = o*'029
I cannot omit this occasion of expressing my warmest
acknowledgments to the local Officials of the Electric and
International Telegraph Company, who, from Mr. Evans, the
Superintendent, downwards, were most courteous and obliging,
and rendered us very efficient aid in the course of our opera-
tions.
The Observatory 1 Olasffow, Nov, 9, 1865.
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Mr, StonCy on the Telescopic Disks of Stars. 45
On the Telescopic Disks of Stars. By E. J. Stone, Esq.
This subject having lately excited some attention amongst
the Fellows of this Society, it may be worth while to recall
what theory really says upon the point.
Theory informs us that if a pencil of homogeneous light
diverge from one point, and after refraction through a lens,
with circular aperture, converge accurately to a focus, then,
instead of a single point of light at the focus, we have a small
disk of light, the intensity of the illumination of which rapidly
degrades to a ring of absolute blackness, then increases to a
ring of maximum illumination, then decreases to a ring of
absolute blackness, and so on for many alternations ; the illu-
mination, however, at the different maxima degrades with such
rapidity that at the first, second, and third maximum, we have
respectively the ^th, -j^rr^^y ^^^ 7^*7^^ ^^ ^^® illumination at
the centre of the disk. (See Professor Airy's Paper, Camb.
Trans, vol. v.) If we call these rings of absolute blackness
and maximum intensity dark and bright rings respectively of
the first, second, &c. order, theory proves that the angular
radii, at the centre of the lens, of a ring of any order, is inde-
pendent of the focal length of the lens, and varies inversely as
the radius of the aperture. The theoretical law of the de-
gradation of the brightness of the central disk is exhibited in
the following table, which is calculated with 0*000022 inch for
the wave length. The intensity at the centre of the disk is
taken as the unit, and the angular distance between the centre
and the first black ring is divided into twenty equal parts, for
each of which the intensity is given.
Table.
ninmiiuitioii.
I •0000
0-3316
0-9903
0-2554
0*9606
0-1879
0-9134
0*1312
0-8503
0*0857
0*7746
0-0511
0-6897
0*0267
8
0*5994
OOIII
9
0*5075
0*0028
10
0-4175
20
0*0000
An inspection of this table shows that for some consider-
able distance from the black ring the intensity of the light
is exceedingly feeble as compared with that at the centre.
Consequently, it by no means necessarily follows from the
theory that the angular diameter of the visible disk varies
Digiti
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46 Mr. Sfqne^ on the Tele9copic Disks qf Slfirs.
inversely as the radius of the aperture. It would be a conse-
quei\oe. of the theory, if the .yis\ble dxA Mways.ei^tended sen-
sibly to the first dark ring, but this is certainly not true, for if
'80, the apparent disk of a' faint star wonld.be as great, under
^hesame circumstances of vision, as that of a bright star.
The visible disk would also vary inversely as the.radius off the
aperture, provided that, under the circumstances of vision, the
theoretical disk, which extends to the first black ring, should
be -always proportionably contracted.
'When an image of a star is formed by ui object-glass well
iBOFrected for spherical and chromatic, (Aberration j the conditions
required by the theory arc <5atisfied, except that the presence
of rays of different wave lengths complicates the phenomena
-by introducing coloured rings which will not be considered
^bere. It would appear, then, that, if we should attempt to
isompare the measures of star-disks made with telescopes of
different apertures, theoi^ would not necessarily requirie these
measures to be in the exact inverse ratios of the radii of the
apertures. It would, however, require that any diminution of
^brightness in the image, any increase of magnifying power
•applied to the telescope, should be followed by a tendency in
-the measures to come out smaller.
The well-known contraction of the images of a star, when
* haze- passes over the star, is one illustration of a diminution of
brightness followed by a decrease in the apparent size of the
disk; and with respect to the effects of increasing the mag-
nifying power, which comes. to the same thing, we cannot do
better than quote some remarjks by -Mr. Dawes, in the Astr.
iVotfA. No. 1552. " The telescopic star-disks do not increase
in proportion to the power employed on the same aperture;
and, consequently, up to a certain limit, the separation of disks
(in his crystal micrometer) increases with the magnifying
power."
At the June Meeting of this Society, Mr. Dawes stated
*^ that he. had often measured the disks. .of stars with a double-
image micrometer forpaed of double . Tefrficting crystal, and
that, under sitjuilar circumstances, he found, the measured disks
to depend. wholly and entirely on the aperture of the telescope.'*
This statement pf Mr. Dawes was claimed as a verification
of the undulatory theory.
I think enough has been said to prove the extreme delicacy
of any attempt to verify the theory by the measurement of
star-disks. >The inquiry is here complicated by our ignorance
of what theoretical ilhunination is under given circumstances
required to constitute the visible boundary of the image.
It would,^;at. leasts ^ neoesaary to:know.more exactly the
i force of, '^yunder.BJjmilar. circumstances," before claiming iitCr.
.DawesV statement as a verification x>fi theory. We ^abouU
tTfiquure taknow. whetherall the observations awere .made .:wiih
•: the. same crystal .micrometer, and. .whether > the. same.eyenpiece
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Mr. &iom^s^m the ,T^i€9€(ffpic JS^hs-^itf Stars. 47
w«s.alw*y8 used, or if dhfi '^yfiij^mi^^ -jware .cl^a^ged r9p ^xXo
.secure I tbid aame mugi^ifyiiPig ^ppw^ qor^e ^iffQreQttel^gCQpi^,
if the law yfi9A found to<hald trjtie Q79r,ftii7,x;4^i»aid^i»Ue i^of^Q
of powers. :If Mr. I^wes ibas 4^7 .•ceur^<;e obeeryfUiicim ioa
the .appai^nt magniliudes of(6itiar*di9k9,'3(beir ^o^blioation .WQuVl
be a great :booo to fill . iuter»0jli^ Au jthfe i^ul^t ^of pjborsioal
opties.
1865, Nov. 7.
In :tbe 4i3cus$(ipnf on, .tbis^paper*
Mr. Pritcbard. asked ;wbe&er. Mr. StQnQ,()oi|si4ered ibat the
diameter, of the spurious difik in .some de^^. depends upon, the
perfection of the object^gJassi ; 4knd whether, if the spherical
aberration in one tele^isope ^were better corrected l^an in< ano-
ther, it would, i<;^^m/)!Q(H2!t4^,^have:a;tQndencj to r^duoe the
size.
Mr. Stone replied in the affirmative.
Mr. Pritchard observed that he had been induced to ask
the question because Mr. Dawes had stated that the size
depended, ccBteris paribus^ entirely upon the aperture, which
was quite in accordance with theory. A conversation took
place between himself and Professor -W.H. Miller, of Cam-
bridge, wherein reference was made to some object-glasses
made by Dr. Steinheiji, who, acoordijig to Professor Miller, had
stated that he had made object-glasses of such, perfect form
and material, that the spurious 'di^k of the stars Jbecame so
large ^ that for douUe-s.tars, which appeared, to be divided when
viewed through ordinary tclescppes, the spurious disks were so
expanded that a dark glass was oeceaifliaiy.to s^e whether they
were divided or not !
The speaker added that the.spupous didk .of 4i star dimi-
nishes v«ry 1 rapidly in brightness towards : the edge, ^o
doubt the more diaphan<»us the n^at^riai, the less light will be
absorbed, and the. larger the ^puriQUS^Iisk will (£K>fa>r) appear;
but the glass must be diaphaiTiaus beyond .all.pre^dent f^r any
one to be able to measure the difference in the size of the disk.
In fact, measurement can scarcely apply to the spurious disk.
It depends partly upon the light of ibe^aky; aiid anyillumina*
tion in the telescope would diminish it. jMr. Pritchard
thought, that, for the purposes of m^asmrement^'We must look
to the .diameter, of the first ring, and>e wo^ld ask whether
Mr. Stone had measured the diameter of the Jbrightest part
of that ring ; and if so, whether it did or did not vary inversely
with the aperture. If it did not, then the undulatory theory
. must be re^^examinedy as ihtt^v waa a residual ^^enomenon' from
< which something wasi-yet . to be4 leacned. ^ Asl far .aa tba ^bfits
of spherical aberration are concerned, he (Mr. Pritchmpd).was
Digiti
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48 Mr, Stone, on Personal Equation
perfectly sure that there never was a tolerable telescope made in
modern times which had the slightest influence upon the dia-
meter of the spurious disk. A telescope possessing an amount
of spherical aberration that would interfere with the diameter of
the disk would be such a telescope as no honest man would
venture to sell, and no skilful man trouble himself to use.
The diameter of the brightest part of the first ring he looked
upon as an experimentum cruets of that part of the undulatory
theory ; he was, therefore, desirous of hearing Mr. Stone's opi-
nion upon the subject.
Mr. Stone remarked, in reply, that he had never made any
such measurement. At the last Meeting some references which
he believed to be quite illusory were made to the question, and
the only object he had in writing his paper was to point this
out. The undulatory theory only referred to the rings of
absolute blackness and maximum illumination, and with regard
to those no doubt it was true ; but as to verifying the theory by
mere measures of the disk, he believed it would be fallacious.
On Personal Equation in Reading Microscopes,
By E. J. Stone, Esq.
In the Monthly Notices of the Royal Astronomical Society
1865, May 12, is an abstract of an interesting paper by Mr.
Dunkin, " On some Peculiar Instances of Personal Equation."
One of these illustrations is obtained as follows : Mr. Dunkin
has selected from the " Greenwich Results" the observations
of Polaris and Polaris S,P.y made by Messrs. Dunkin, Ellis,
Criswick, Lynn, and Carpenter, all experienced observers;
from the discrepancies of the results of the observations made
by each observer above and below the pole, Mr. Dunkin has
deduced corrections to the adopted colatitude, and has consi-
dered each observer to have his own colatitude.
The results thus obtained are as follows : —
o '
From Mr. Dunkin's obsenrations 38 31 21*81
„ Mr. Ellis's „ 38 31 22*01
,, Mr. Criswick's „ ... ... 38 31 2i*9»
„ Mr. Lynn's „ 38 31 21*64
„ Mr. Carpenter's „ 38 31 21*48
The difference between the results thus obtained from the
observations of Messrs. Ellis and Carpenter is seen to amount
too"-53.
Digiti
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in Reading Microscopes. 49
On the night this paper was read, I offered to the Meeting
what I considered the explanation of these anomalous results,
an explanation, however, perfectly in accordance with the
general result of Mr. Dunkin's paper " that personality does
exist in the reading of microscopes," and, in fact, a neces-
sary consequence of the existence of such personality; and
finding that explanation borne out by a numerical inves-
tigation, I have thought it worth while to place it on record.
The stability of the Greenwich Transit Circle is such that
the reading corresponding to the zenithal position of the telescope
remains sensibly unchanged for considerable periods of time ; it
has been usual to put together all the determinations of zenith-
point reading made in a fortnight, and to adopt the mean re-
sult for the zenith«point reading in the reduction of all obser-
vations made during that fortnight.
The observing with the Transit Circle is distributed with
great regularity amongst the assistants. If therefore, we call
the differences of habit in reading the microscopes between any
one observer and the mean habit of all the observers the personal
equation of that observer, it will follow from the course adopted
at Greenwich that the adopted readings for the zenithal posi-
tion of the telescope will be free from personal equation, but
that the resulting observations in N.F.D. will be affected with
the personal equation of the observer, consequently the differ-
ence between the reading corresponding to the zenithal posi-
tion of the telescope and the reading corresponding to the
polar position of the telescope, as determined from the obser-
vations of any one observer, will be affected with the personal
equation of the observer in opposite sign.
If this explanation is correct, the mean of all the results,
which is the colatitude adopted at Greenwich, is free from the
error of personality, and of course if the same observer deter-
mines the zenithal position and polar position of the telescope,
the colatitude is free from personal equation; this is on the
assumption that the observer's personal habit does not sensibly
change in reading off different divisions of the circle.
In order to test this explanation numerically, I have found
the differences between the nadir- point determinations made
by Messrs. Dunkin, Ellis, Criswick, and Carpenter ; to do this
I have compared all the derminations made by these gentlemen
during the year 1861 and 1862. I find
Mr. Dunkin's Reading for Nadir — Mr. Ellis's ditto = + 0*30
„ „ — Mr. Criswick'g ditto — + 0*04
,, ,, — Mr. Carpenter's ditto » — 0*35
There were not a sufficient number of Mr. Lynn's observa-
tions to determine his personal equation.
We thus have for the person^ equations,
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50 Mr. Stone, ott- Ptneftal Equkation, Sfc.
D. s o'oo
EL = + 0-30
C. = + 0\>4r
JiG. ».— 0-35
And applying these results,, with changed signs,, to the colati-
tudes dedjuced by Mr. Dunkiny wa haws for the resulting .c(dati-*
tudes,,
F^oitt MvL DliAkiii's ^>bi^i¥iCidtii ' 3^ 34^ 21's^i
„ MtlBflisV „ 3f8 31 2171
„ I8f K Cridwtek's „ ^8 31 2t8'8
„ lilr: Carpenter's „ 38 31 21*83
The agreement between ttiese i^esahs* is very dose indeed.
It appesM tbfat Mr. EUis's^afRd Mr. CM-pefit^r'8> habits of read-
ing mierosoopes, although t^rj different; d6 not sensibly vary
\Hl;h tlie part- of thel circles used. It may be mentioned that
Mr. CarpentiBir is^ longer sighted tAum^ Mr. Lynn, Mr. Lynn" than:
Me8tt«. Dunkan and Giiswiek^ and' Messrs. Dunkin and Cria*
wick than Mr. £Hi9. It is impo'ssible, on acoonnt of changes
of tempeiratare, to keep 1^ gradoadons^ of tkff cirde and> the
micn>scope-wir«s alwayi^ at the same tkne perf^Iy in focns. I
am inclined to thbik that the amount of personality in reading
the mier<9Scopes would bo much diminished, if Ihe wires- and
graduations* ite»« aHways seen under' exactly simillur* optical
circnmstaneesi
Upon Uie qjuestion of Personal Equation* seioe disoastton
took place.
Mr. Pritchard mentioned the case of a gveat practical phi-
losopher whom he had known^ who was not able to bisect
twice runnii^ within three seconds, a&d he doubted whether,
anybody in the room not habituated to observe^ would be able
to- avoid a^ similar mistake. On the other hand, he had tested
the eyes of the late Miu Andrew Ross, the microaoope-maker,
some years ago^ Mr. Ross was not accustomed to astro-
nomical observations, and yet he bisected a division of a circle
ten times, without making a difference of a i oth of a second.
Professor Challis mentioned an instance of an assistant at
the Cambridge Observatory, who was a very good and con-
sistent observer, but in bisecting with a microscope his results
were always erroncfous, about -p*^ or -/j of a second.
Mr. Dunkin gave another noteworthy instance, which came
under his eye oidy a few daya previou^y ; and at the
end of the discussion whieht took place upon the subject^ Mr.
De La Rue concluded by ealHiig attention to the importance
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Mr. Herschely on ttadiant Points of Shooting- Stars, 51
of nfiakirig slicli cbmpaHsQh'd sb ad to eliminate personal error.
We W^re tod apt to look upon graduated instruments as lettding
to aliiibst' absolute petfectioh ih observation. Biit* we must
alWays'beJtr* in' mind that tli6 eye forms part of the instrument
arid nitist^tatke' that into coiisidcira^tioti;*
Radiarit Points of Shooting- SttCrii. By A. S: Herschel, Esq.
The fdllowing reiriArks relate to a itoeteoricf slidWer of some
irilfensity; jtnd displaying a i*eifiarkably radiants diefiinite pbint,
observed at Hawkhurst on the 20th of October^ 1865*.
On the nights of the 1 6th- 1 8th of October, the sky at Hawk-
hurst was overcast, with constant rain. On the night of the 1 9th,
a watch wiis kept for forty-five minutes, until eleven o'clock, but,
althbugh the sky was clear, without seeing any meteors directed
frdhi thb known radiant point in Orion, On the night of the
20th the sky was cloudless, and on the watch being resumed, the
* An art^ of celebrity expresses a doubt reginrding the e:xistetiidB of p«f -
sonal equation in the estimation of the bisection of a division of a circle. A
reading microscope, frefe from parallax, is in process of construction; great
attention ^111 be p»aid to the cleanness of the cut, to the illumination, and to
thte i^e^ation of the emer^nt pencil ; and tlien the Members of thfe Society
wiU l^ able to make the experiment themselves at an evening meMing,'^
[C. P.]
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52 Mr, Herschely on Radiant Points of Shooting^ Stars.
occurrence of this meteoric shower was immediately apparent.
Owing to their leaving remarkably luminous streaks, the tracks
of nineteen meteors, described in the following list, could be
noted among the stars with somewhat more than ordinary pre-
cision. Projected upon a plane-perspective planisphere of the
sky (see figure), haying the zenith of Greenwich for the centre
of the projection, these nineteen tracks, with three exceptions,
when prolonged backwards, pass through a small circle having
a radius of only four degrees, and having its centre situated at
f Orionis, in R. A. 90°, N. Decl. 1 5°. In the following table
the deviation of each meteor from the general radiant point; or
the least distance of the great circle of its apparent path,
prolonged backwards, from this pointy is given in the last
column of the table : —
Mag.
No.
O.M.T.
1865.
Oct. ao.
Comp"* Length
Stan. Path.
streak
Dura- Dara-
tion. tion.
Began.^
R.A. Decl.
Ended.
N. ]
R.A. Decl.
Devia-
tion.
1
h m
10 30
9
Bee-
0-4
tec.
185
69
210
6|
2^.8
2
10 43
H
07
...
53
40
-5
3-0
3
10 58
9
08
67
H
58
12
2-8
4
II 6
21
0-8
125
61
17'
70
©•2
5
II 19
15
07
92
29
95
45
0'2
6
II 22
39
0-9
'5
46
333
37
%'o
7
II 31
30
0-8
16
35
342
28
O'l
8
II 36
'3
o*6
81
32
73
44
0-4
9
11 40
41
0-9
70
66
297
70
0-6
10
II 41
22
07
84
68
17
89
3-0
II
11 43
18
0-6
17
89
276
73
4-0
12
II 48
^4
08
38
17
-7
0*2
>3
II 54
26
0-7
33
39
357
37
©•o
H
12
16
0-5
»3
40
2
38
o*o
J5
12 4
17
0-6
322
70
303
56
95
16
12 18
9
0-4
101
59
109
68
1-8
17
12 25
6
0-4
...
95
45
99
60
1*2
18
12 29
17
0-6
164
62
201
61
5-0
19
12 33
8
I'O
...
130
29
141
29
6-0
Average
Values
19
0-68
1*3
2*2
The mean deviation is
2^-2:
but if the
three most
per-
turbed of these nineteen meteoric tracks
(Nos
. IC, ]
[8, and 10)
are omitted, the mean <
of the sixteen remainin
deviation from the
ig meteors is only
general radiant point,
i°-4. The deviations
of fourteen meteors from their common radiant point, observed
on the 1 8th of October, 1 864 {vide Monthly Notices for 1 864,
December 9), were in the same manner as follows : —
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Mr. Her9chel^ on Radiant I\nnts of ShooHng- Stars. 53
R«f.
No.
Devia-
tion.
Bef.
No.
Devia-
tion.
Ref
No.
Devia-
tion.
Ref.
No.
Dovla-
tiOD.
I>
»^8
5>
30
9.
1^8
I3»
I'S
a»
»-5
6,
0-4
10,
60
I4»
OS
3»
4>
0-3
7,
1*7
3-0
II,
12,
10*6
7-»
Mean 1
Deviation J
a-9
If the three most perturbed of these fourteen meteoric
tracks (Nos. 10, 11, and 12) are omitted, the mean deviation
from the common radiant point of the eleven remaining meteors
is only i°*6. Collecting together the results of both years*
observations, we are thus enabled to give the position of this
radiant point in the following definite, tabular form : —
ntO. Portion. No. of Mean
Date of N. Meteors Devla-
Observation. R.A. Deol. Obeerved. tion.
00 o
1864, October 18 90 16 11 1*6
1865, October 20 90 15 16 1*4
As the meteors of this shower will probably be observed
every year, it will be interesting to ascertain if the radiant point
so distinctly marked, and apparently so fixed, will in future
undergo any alteration in its position. A few bright meteors
were observed at Newhaven, U.S., by Herrick, on ihe nights
of the 20-26th of October, 1839 (vide Am. Jour, Sci.\ and
were described by him as radiating from *' near i Geminorum.**
This position is more than twelve degrees from the place
assigned to the present radiant point. It is not impossible
that the radiant point of a meteoric shower may have altered
its position to this extent in the course of nearly thirty years.
Connected with the question of the possible motion of the
radiant point, every available means will be taken by the Lu-
minous Meteor Committee of the British Association^ to deter-
mine as accurately as possible the position of the radiant point
of the November meteors, on the occasion of their expected
return on the morning of the 13th of November, 1 865.
The November Meteoric Shower* By J. Glaisher, Esq. F.R.S.
[This was a verbal oommunication to the Meeting.]
At the last Meeting of this Society, notice was given by
the President that a recurrence of the November shower
of meteors was expected on the 12th of November. I be-
lieve that notice was responded to by a very large number of
observers, who looked out very assiduously till the hour of 1 2,
and then retired without occupying themselves at all about
B
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54 ^'T' Glaisher, The November Meteoric Shower.
meteors afterwards. I am not surprised at this. It is the
custom of the Astronomer Royal to enter in a pocket-book,
before the end of one year, all phenomena to which attention
is to be paid in the following year ; and if we look into these
pocket-books, we shall find in every one of them, as far back
as 1836, entries on certain days, " Look out for meteors ;" and
if we look into the Greenwich volume of Observations for the
observations of meteors on those days, we shall find very few
recorded ; yet on every one of these days I have charged
observers to keep a good watch on certain parts of the heavens,
until at last I was almost ashamed to do so, and almost con-
cluded that the shower-meteor theory could not be sustained.
On the night common to the 12th and 13 th of November
a' watch was kept up at the Royal Observatory, Greenwich,
from the hour of 6. Between this hour and S'* two meteors
only were seen ; from 8** to 1 2^ the sky was cloudy and no
meteors were seen. At this time six observers (viz., W. C.
Nash, A. Harding, F. Trapaud, E. Jones, T. Wright, and
Lieut. Rikatcheff, R. I. N.) were located on an elevated part of
the observatory. At 12 minutes after midnight the clouds
began to break, and at 20 minutes to i the sky was free from
clouds. At I o'clock the paths, 2ones, colour, and other par-
ticulars of 29 meteors, were recorded. By 2^ a.m^ the same
particulars of 70 additional were noted ; and by 5** a.m. the
positions, &c. of nearly 280 meteors had been secured. Before
this time we knew that we had abundance of observations to
determine the radiant point, or points; and for a space of
nearly a quarter of an hour the paths of the meteors among
the stars, &c. were not noticed, but their number was simply
counted. The result was that at this time meteors of the first
class were appearing at the rate of 250 per hour. Now for
every meteor observed, there were at the lowest estimation two
or three whose positions were not recorded ; so that at least
1000 meteors were visible during the hours of i to 5 o'clock.
At the hour of 5 the Moon was shining brightly, and many
meteors were seen close to her.
Mr. Alexander Herschel was observing at Hawkhurst till
nearly 3** a.m., and he noted the positions and paths of 68
meteors, which he has laid down on a diagram, indicating very
clearly a well-marked, radiant point in Leo.
Many of the Greenwich meteors are laid down on this
diagram, and by comparing the two diagrams together it will
be seen that the Hawkhurst diagram indicates the radiant point
in Leo, within narrower limits than the Greenwich diagram.
Also it will be seen that more than one radiant point is indi-
cated in the Greenwich diagram ; but they are in the same
right ascension, viz., about lo**. Now the great interest con-
nected with this part of the results, in relation to astronomy,
is that this position in Leo is the part of the heavens towards
which the Earth was moving at this time ; and apparently, as
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Mr. Glaishevy The November Meteoric Shower. 5 5
soon as the Earth approaches this part of the heayens, those
bodies situated there become luminous. This adds another link
to the sciences of Astronomy and Meteorology.
I think there is no doubt that the meteors observed this
night were those of the November period. At Greenwich, for
more than twenty years, a good look-out has been kept for the
annual display of shooting-stars at the November period, but
this is the first time we have seen them. It is very likely that
on several occasions we have closed our watch too early. It
was the knowledge of this fact that made me say, at the begin-
ning of these remarks, that I was not surprised at gentlemen
giving up watching at 1 2 o'clock ; for it is no joke, as I know
by experience, to stand motionless on a clear, cold night, hour
after hour, staring, as it were, at vacancy, with perhaps one
or two observations only as a reward. It is also likely that on
some occasions the shower has taken place during the day, and
therefore has not been visible at Greenwich at all.
Speaking of radiant points, I may remark that there are
56 already determined and well marked. Many of these deter-
minations have been materially icfiuenced by isolated observa-
tions of meteors observed on the same day in different years
being brought together, thus indicating the same point of the
heavens as the origin of the meteors. I know nothing in phy-
sical research which seemed so unpromising as isolated observa-
tions of shooting-stars did a few years ago, yet how well a patient
and painstaking record of such phenomena has been repaid.
The next step in the reduction of the observations of these
meteors will be to ascertain those which have been doubly
and trebly observed, so to determine their heights and velo-
cities.
The only information I can give to-night in these respects
is that with whichMr. A. Herschel has furnished me. It
appears that 1 5 meteors observed on that night by Mr. Herschel
at Hawkhurst were simultaneously observed by Professor
Adams at the Cambridge Observatory. The distances from the
Earth, at the beginning and end of the apparitions of five of
these doubly-observed meteors, were as follows: — 75 miles and
54 miles ; 72 miles and 55 miles ; 68 miles and 44 miles ; 89
miles and ^7 miles ; and 1 14 miles and 85 miles.
These distances are somewhat greater than usual. I con-
sider it of great importance to get simultaneous observations of
other meteors ; and I hope that our knowledge of the distances
&c. of these bodies will be much increased by the observations
of this night.
Mr. Pritchard : There is one matter I would* ask Mr.
Glaisher to state to the Meeting ; of course the number
visible of these shooting-stars depends upon the radiant point
being above the horizon ?
Mr. Glaisher: Yes.
Mr. Piitchard : And therefore these observations prove
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56 Mr, GlaisheTy The November Meteoric Shower,
how correctly the position of this radiant point is known,
because, from what I gather from your communication, it ap-
pears that the maximum number of meteors occurred just at
the hour that was foretold.
Mr. Glaisher : It was within one hour or so. The hour
foretold was from 1 2 to 1 a.m. ; two-thirds of that hour was
cloudy. I think the President, at the last Meeting, recom-
mended looking out for an hour or two before and after the
hour of 12. I may mention that a fine display is expected on
the 13 th of November next year.
Mr. Fritchard : Did you see the maximum number of me-
teors about the time when the point of the heayens towards
which the Earth was moving appeared above the horizon?
Mr. Glaisher : Most certainly ; and I may add that in the
six hours preceding midnight on the 12th, we saw only two
meteors, and in the six hours preceding midnight on the 13th,
with a cloudless sky, two meteors only were seen; thus it
would seem that both before and after this time the meteors
were scarce.
Mr. Fritchard : What time did that part rise ?
Mr. Glaisher: Before midnight; it would be about six
hours from the meridian at midnight and about two hours
from the meridian at 5 in the morning.
Mr. Fritchard : And your maximum was seen somewhat
after midnight certainly.
Prof. Challis: What Mr. Glaisher has said confirms my
experience at the Cambridge Observatory. I often looked out
for the November meteors, but could not see them. I had
seen the August meteors very regularly with no very great dis-
proportion as to the numbers; but I cannot say that I saw
anything more on the 12th November than on other nights.
Professor Adams has given me the particulars of his observa-
tions last 1 2th November. He begun at 1 2 o'clock, and went
on to about 20 minutes past i, and during that time I think it
was 120 — at all events, above 1 00, that he saw. My expe-
rience of the August meteors has been this, that I never at
that hour of the night got that number; so that it is quite
clear, from the experience of the Cambridge Observatory, that
the appearance of this last November is exceptional — a kind
of shower such as we have not noticed before. I may also,
perhaps, state that Professor Adams told me that he found
fourteen coincidences — I think twelve certain — by comparing
with Mr. A. HerscheFs observations : and that the average
height of the meteors they ascertained was 83 miles. I men-
tion this because, in the year 1 862, I took observations myself
in the August period, and compared them with observations
made at Hawkhurst on that occasion, and we got an average
height of 82 miles. The number of coincidences is ten ; and I
think the coincidence of heights at the two periods is remark-
able and worthy of notice.
Digiti
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Mr. Talmage^ Observations of OccuUations of Stars. 57
Mr. Frideaux said that on the night in question he had
gone with two companions to the top of Primrose Hill, and
that in the forty minutes they remained there they saw seventy-
two meteors. His friends were perfectly inexperienced in the
matter. They arrived there about 3 oVlock in the morning.
During the whole of the time that they were out, somewhere
about an hour and a half, they saw nearly 1 20 meteors.
Observations of OccuUations of Stars by the Moon, and Phe-
nomena of Jupiter*s Satellites, made at Mr, Barclay's
Observatory, Leyton, N.E. By C. G. Talmage, Esq.
1865, June 28. Transit oi Jupiter's First Satellite.
Egress.
h m •
6.M.T. Central bisection = 10 31 3 a
Last contact s lo 33 23
1865, July 5. Disappearance of 8 Librce.
G.M.T. » 9*44"'4S*45 *
Disappearance of ** Libra.
h m •
9 58 4*24 Mr. Barcla]
9 58 6*24 Mr. Talmage d
h m •
G.M.T. 9 58 4*24 Mr. Barclay c
1 865, July 3 . Reappearance of 8 Libra.
G.M.T. io«»48»29«-46 e
Beappearanc^ of «^ Libra,
G.M.T. io"»5i'n22«-49 /
1 865, July 8. Occultation of { Sagittarii.
h m •
G.M.T. Disappearance » 9 21 19*13 g
Reappearance sio xi 30*88 h
1865, July 25. Fclipse : Reappearance oi Jupiter's Second
Satellite.
G.M.T. ip'»4i»o»-6o *
m
Digitized by VjOOQIC
58 M.Moesta^ Observations of the Comet III, i860.
1865, July 26. Eclipse: Reappearance of Jupiter's Third
Satellite.
G.M.T. 8'»44'»32»o8 /
1865, July 29. Eclipse: Reappearance of Jupiter's First
Satellite.
G.M.T. ioi7»i9»'43 m
1 865, Nov. 4. Occultation of 3* Tauri.
h m a
G.M.T. Disappearance 9 57 56*93 n
Reappearance 10 36 43*06 o
a, Jupiter low, but the satellite was well defined.
b. Observed with the large refractor of 10 inches aperture, with a power
of 137 ; time exact.
c and d. Mr. Barclay observed the disappearance of this star with the
large telescope ; but he thinks the time a little doubtful. I observed it with
a small telescope of 3^ inches aperture, placed in the garden ; and I feel
confident in the time being exact.
e and/. Both stars came out very sharp at the times ; the night was very
clear. The colours of the stars contrasted very strongly, «' Libra being
almost white and 8 Libra grey.
g and h. The star did not disappear instantaneously, but hung on the
Moon's limb for nearly half a second, or rather it seemed to be dongated
considerably. The time of reappearance is exact.
k. Observed with a power of 220 on the equatoreal; very clear and
steady.
/, m, n, and o. The times are exact.
The eclipse of the Moon, on the 4th of October, was well
seen here, but no attempts were made to take time observa-
tions ; the dark limb of the Moon was apparently surrounded
by a luminous streak, as noticed by Mr. De La Rue ; but it did
not disappear on applying higher powers; the highest used
was 350, on the lo-inch refractor; this was remarked by Mr.
Barclay as well as by myself.
Observations of the Comet III, 1 860, made at the Santiago
Observatory, Chili, By C- W. Moesta, Director of the
Observatory.
I beg leave to transmit a series of observations of the
Comet III. 1 860, some of which were, I believe, sent in the
year 1861. Those observations were made with a 5 -feet
Equatoreal, to which was adapted a ring-micrometer ; but as
Digiti
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M. Moesta, ObservaHans of the Comet III. i860. 59
at that time the new building of the Observatory was not
finished, the instrument could not be mounted equatoreallj,
and could only be placed provisionally on loose ground in a
room, provided with a prime vertical opening. On account
of this circumstance, I consider the enclosed observations of
no great value ; still, if the Comet should not have been
observed at that time elsewhere in a better way, it might be
deemed proper to publish them.
iseo.
July 21
Santiago
Mean Time,
h m ■
7 10 49*3
Am,
Comet— Star,
m s
+ 5 39-17
No. of
Comps.
2
Comet— Star.
No. of
Comps.
Comp
Star.
1
a4
6 35 27'9
+ 3 49'i8
3
...
...
2
as
6 53 59-2
...
...
+ 44 i8-7
2
4
Aug. 13
9 50 27*6
+ 6 i6'29
2
+ 40 185
2
5
10 10 25*9
-10 4-87
Z
...
6
17
9 ^3 59-0
- S ^S'S^
2
...
...
7
10 4 32-4
...
+ 47-6
2
7
10 10 21*2
...
+ 37 35*7
I
8
18
9 17 IO*8
+ 4 4270
3
...
...
8
9 45 36-4
...
...
+ 41 43-8
3
9
20
9 6 53-2
+ 3 58-87
3
...
...
10
9 3' 57-a
...
- I 43*1
2
10 +
9 SO S7-I
...
- 50-5
2
10—
as
8 54 28-6
+ 311
3
...
II
8 54 a8-6
- a 59*39
3
...
12
9 35 12-2
- 2 55-19
2
...
...
12
9 a> 3*7
...
+ 7 X4-3
12
Sept. 6
7 58 34-7
- 2 51-29
3
...
«3
8 39 I3-I
...
- 51-3
2
13 +
8 57 14-9
- 12-4
2
13-
7
8 4 27-2
- 40-88
I
...
...
»3
8
8 32 36-3
+ I 37-00
I
...
...
10
9 10 21*5
...
...
+ 39 4-8
2
17
IX
7 44 4-6
- 6 34-31
2
...
18
8 16 45-7
...
...
+ 6 8-2
I
18
8 33 197
...
+ I 58-9
I
19 +
845 8-8
...
...
+ 2 44-8
2
19-
12
8 843-8
...
...
+ 8 1-8
2
20 +
8 27 i6-8
...
...
+ 7 S9'i
2
20—
M
7 26 23-8
— 1 16-64
2
...
...
21
7 45 46-'
...
...
+ i8-o
2
21 +
8 4 29-3
...
...
+ I 17*2
2
21 —
The signs + and — in the last column indicate that the comet and the star
were obseired on both sides of the centre of the micrometer.
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6o Rev, T. Chevallier, Observations of Solar Eclipse.
Mean Places for iSSi'O of the Comparison StarSy
Deduced from the ObseiratioiiB made with the Meridian Circle at Santiago.
No.
Star'tNune.
Ma«.
R.A.
D«el.
IaS.A. InDed.
I
Arg. 0. II 8 30
H
h m •
" S3 44-93
# #
-18 53 7-2
3 060
20-05
ft
Lacaille5i25
7-6
12 15 46-41
—24 6 6-0
3-031
20*01
4
B.A.C. 4253
5i
12 30 20-37
—26 22 12-6
3-160
19-88
5
V Centauri
4
13 41 11*12
-40 59 360
3-569
18*13
6
X Centeuri
3i
13 57 34-71
-40 30 41-5
3-633
17-48
7
Anon.
7
14 4 52-48
-41 48 34-2
3690
1715
8
Lacaille 5809
7
13 57 37-04
-42 25 24-5
3-672
17-47
9
Lacaille 5826
6
14 1532
-42 48 27-9
3-692
17-36
lO
Anon.
8
14 3 5482
—42 42 II-6
3-707
1719
II
Lacaille 5918
7
14 15 51-40
-43 40 34-4
3-785
1663
12
Lacaille 5943
7
14 18 54-12
-43 4» 6-5
380
16-48
13
Anon.
7i
14 52 28-91
-46 27 2-7
4-033
14-64
17
Anon.
7
14 57 5»-«3
-47 45 a6-3
4-103
14-31
i8
Lacaille 6279
6
J 5 7 14-59
-47 20 46-1
4-13
13-73
*9
Anon.
10
14 58 43
-47 17
20
Taylor 8002
7
15 6 3886
-47 31
4-134
21
Taylor 7997
...
15 6 1503
-47 33 "-I
4-133
13-79
June %, 1865.
Observations of Solar Eclipse October 19, 1865.
By the Rev, Temple Chevallier.
I send the observed time of the first contact of the Solar
Eclipse of October 19, 1865, made bj Mr. M. R. Dolman,
observer, for insertion in the Monthly Notices.
Solar Eclipse, October 19, 1865.
Obsenradon of Time of First Contact, made at the Observatory,
Durham.
1865, Oct. 19, 4»» 7» 34»-7 Greenwich Mean 'feme.
Good Observation.
M. R. DOLII AN.
Durham Observatory, Nov. 15, 1865.
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Lieut. AshCy FhysUal ConstituHon of the Sun. 6i
Note on f Herculis, By T. W. Burr, Esq.
In the last number of Vol. XXV. of the Monthly NoticeSy
Mr. Fletcher draws attention to the fact that the above star,
which with his large refractor is now " absolutely single," was
a few years ago measurable with a telescope of 4 inches aper-
ture only. This reminded me that I had seen it double with
even less aperture, and thinking the period of this observation
might be interesting I have referred to my note-book, and find
that on the 19th May, 1853, I saw the pair well separated
with a power of 480 on my Ross Equatoreal of 5-|*in. aperture,
and that even with 173 the duplicity could be detected.
I did not apply the micrometer then, but some measures by
Mr. Miller in the Notices for the same month gave i"'4 for the
distance.
ItUngton^ Dee, 7, 1865.
Physical Constitution of the. Sun. By Lieut. E. D. Ashe,
Director of the Quebec Observatory.
The author states that his observations were made with a
telescope of 8 inches aperture, 9 feet focal length, mounted
equatoreally, driven by clock-work, and being one of Alvan
Clark's superior telescopes. The power generally used waa
400. He also states that the atmosphere of Quebec for
astronomical observations is not second to that of Italy. He
remarks that there are difficulties to overcome in the cavernous
view of the question that he thinks are insurmountable.
He explains his own theory as follows: — I conceive the
Sun's surface to be composed of an equally bright and incan-
descent photosphere, that our Sun is a nebulous star, and that
the nebula consists in what is seen as the zodiacal light ; that
the spots are small meteor planets that revolve round the Sun,
and that they fall into it ; at first they are not visible even to
the largest telescopes, but after they meet and spread out they
cover comparatively a large surface. When they crack and
split into pieces they show the bright surface of the Sun called
bridges ; that the penumbra is the dross or thinnest portion of
melted matter, which when further attenuated breaks up into
patches, and finally forms the darker portions of the granula-
tions that cover the surface of the Sun. The faculae are nothing
more than the disturbance of this scum, showing the brighter
portion of the Sun's surface, which disturbance must take place
in the neighbourhood of these boiling, melting masses ; also,
that there is a drift, as mentioned by Mr. Canington, which
Digiti
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62 Rev. Padre Secchi, Observations of Double Stars,
carries the facul® awaj and distributes the ecum over the
entire surface of the Sun. And he adduces arguments, sup-
ported by references, that may sustain his view of the question.
M. Chacomac, in a letter dated 24 October, 1865, addressed
to the President of the Society, refers to the continuation of
his researches on the physical constitution of the Sun ; and
states that after various observations he has arrived definitively
at the conclusion that the Sun is at least as luminous at its
centre as in the brilliant envelope which bounds its visible con-
tour ^ que le Soleil est au moins aussi lumineuse a son centre
que dans cette enveloppe resplendissante qui limite son contour
visible").
Observations of Double Stars, By the Bev. Padre Secchi.
July 20, 1865. I measured the star i Cygniy and found
P = 348<>-45,D=i''-465.
July 20, 1865. y Coronm is round only occasionally; it
seems there is a notch in direction 85°.
I HercuUs likewise is round ; in the best moments a notch
appears in the disk on Dir. 3 1 5°.
51 iLtbroiy A.B., Pos. = 155°, Dist. o"-40, disks well
separated.
Borne t Nov, 24, 1865.
The Society has received from Mr. A. Brothers a sheet of
photographs of the Moon, taken during the Eclipse on the 4th
Oct. with his Equatoreal telescope of 5 inches aperture. Mr.
Brothers writes that the prints must not be looked upon as
photographs of the Moon, as many very much superior have
been taken, but merely as pictures of the Eclipse. The atmo-
sphere was so much disturbed during the whole time of the
Eclipse that the sharpness of detail is lost to a great extent.
He attempted to obtain the entire outline of the Moon, but
failed to get more than greater sharpness of the shadow ; this
will be seen in No. i o, which was exposed 1 5 seconds ; Nos.
8 and 1 2 were exposed 3 seconds, and the remainder from 1 to
about 2-tenths of a second.
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Capt. Noble, Occtdtations of Stars by the Moon, 6$
Observations of Encke's Comet, By G. R, Smallej, Esq.
{Extract of a Letter addrened to the Artronomer Royal,)
I send the approximate places of Encke's Comet, deduced
from four sets of observations (such as thej were) in June and
July last. There were but four nights when I could see the
Comet at all, and then observation was most difficult, and, from
the absence of anj appearance of condensation, bisection almost
impossible.
Hitherto I have had no means of identifying the stars of
comparison, and the results I send you are corrected for refrac-
tion and instrumental errors only.
Approximate Places of Encke's Comet (corrected for refiraetioii},
1865.
Date.
Mean Time.
B.A.
Soath
Jane zs
h m B
7 14 69
h m a
8 26 19*8
/
to 49 2*0
29
7 4 59-0
8 34 59-3
12 58 545
30
July I
7 18 39*7
6 51 06
8 44 14s
« 54 13-3
IS H 56-5
17 3a 36*6
Comet very faint throughout.
No appearance of any nucleus or tail — a mere faint patch of haze.
Government Observatory^ Sydney,
Sept, 22, 1865.
Occultations of Stars by the Moon, observed at Forest Lodge,
Maresfield, By Capt. W, Noble.
Monday, July 3d, 1865.
8 Libra,
The star disappeared instantaneously at the Moon's dark
limb
at i6h 33»n 5o»-3 L.S.T. = 9* 46'" 8»'7 L.M.T,
and reappeared at the bright limb
at 17^ ss™ 48*4 dh*L.S.T. .« io»» 47'" $^'7 ±L.M.T.
«^ LibrcB disappeared instantaneously at the Moon's dark
limb
^ at i6h 47» 26»-8 L.S.T. « 9.'» 59» 43»*o L.M.T.
Digiti
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64 Lord WroUesley^ Observations of the
and reappeared also instantaneously at the Moon's bright limb
at i;*" 39" 13*0 L.S.T. « lo"* 51™ »o»7 L.M.T.
At the times of emersion the bubbling and boiling of the
air was very great, and this renders the reappearance of
8 Libra slightly uncertain.
Power employed 1 3 5 upon the micrometer, with of course
a positive eye-piece. It was adjusted upon the stars.
Saturday, Noyember 4.
^ Tauri.
The disappearance was not observed; but the reappearance
took place instantaneously at the Moon's dark limb
at I* 34» 4»*5 L.S.T. « io»» 37™ ii»-8 L.M.T.
Power 255 adjusted on the star.
Sunday, November 5.
115 Tauri,
The star disappeared somewhat sluggishly at the Moon's
bright limb
at i«» i9» i7«'9 L.S.T. - i8»» 8« 43«-4 L.M.T.
The reappearance was not observed.
Power 255 adjusted on the star.
In each case the telescope employed was my Ross Equa-
toreal of 4*2 inches aperture and 61 inches focal length.
Forest Lodge, Maresjield, Uekfield,
November 9, 1865.
Observations of the Solar Eclipse^ October 19, 1865.
By Lord Wrottesley.
The commencement of the Solar Eclipse of the 19th of this
month was here observed to take place at 4** 2"* 3* Wrottesley
Mean Time. Instrument, the i i*feet Equatoreal; observer, Mr.
Hough.
The observation was not very satisfactory, as the eye of
the observer was not directed to that part of the limb of the
Sun, on which the first impression was made, at the instant of
Digiti
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Solar Eclipse. 65
contact ; but Mr. Hough is satisfied that the time above given
is not more than 6' too late.
The Sun was at times obscured bj clouds, and the limbs of
both Sun and Moon were exceedingly tremulous. The two
great spots near the edge of the limb added much to the interest
of the phenomenon.
Wrotieiky, Oct. %^, 1865.
Notice of a recent Memoir of Prof Krueger^ of HeUingfors^
on the Star'cluster in A Persei, B7 R. C. Garrington, Esq.
Prof. Krueger has recently sent copies to this country of
the memoir above named, and accompanying my copy has
written me a request that I would call the attention of the
Society to a conclusion to which his researches have led, and
which he considers to require re-investigation by an indepen-
dent person. Regarding the example of Bessel in very care-
fully recording the relative positions of numerous principal
components of the Pleiades as one to be followed in other simi-
lar cases, he has in similar manner by heliometric observations
ascertained, and placed on record the relative positions of 43
stars in A Persei, by referring them in distance and position to
a double star d which he took for his zero-point ; and a cata-
logue and chart and particulars of redaction and theory are
appended. He has further divided his results into two groups
of Spring and Autumn, results between which a difference
comes out which would (if no instrumental influence vitiates
the conclusion) imply a position parallax of the cluster of -Irds
of a second as referred to the double star, or that the double
star d the components of which are of the ninth magnitude
is situated considerably behind the cluster of which optically
it appears a component. As there is an inherent improbability
attached to this conclusion, Professor Krueger suspends his
judgment till he is able to further examine the question, and
lays the result before others as an interesting case for inde-
pendent investigation.
It needs no remarks from me in addition to his own to urge
the desirability that this should speedily be done by those who
possess the opportunities and necessary qualifications for so
delicate a research ; but I would take the opportunity of re-
marking that several other clusters ofier similar fields of useful
labour to those members of the Society who, though not pre-
pared to enter on researches requiring many continuous years
of application, are yet willing to take up subjects of more mo-
derate extent.
Dee, 1865.
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66
The Time-signalling Operations at Glasgow. B7 Prof. Grant.
The FresideDt at the conclusion of the Meeting, called
upon Professor Grant of Glasgow, who was present, and who
has been making some successfal experiments in distributing
time over the city of Glasgow, to give an account of his opera-
tions.
Professor Grant stated that, in the time-signalling opera-
tions at Glasgow, Jones's method of regulating clocks is ex-
clusively used. It is generally known that, according to this
method, the electric fluid is employed merely as a regulating
agent, and not in any case as a motive power, the time-piece
under control being an ordinary clock, connected by a regular
succession of electric pulsations with the normal mean-time
clock of the Observatory. The application of the invention in
Glasgow has been perfectly successful. It has been employed
under various forms ; but what Professor Grant considered to
be the most suitable to the requirements of a large city was
the small clock with a seconds' pendulum and a dial of about
3 feet in diameter, showing the time to hours, minutes, and
seconds. Clocks of this construction have been set up in the
public thoroughfares of Glasgow, and have been found to be
exceedingly useful. Attached to each of them is a galvano-
meter, which, by its deflections, gives an indication of the
electric currents transmitted in successive seconds from the
normal mean-time clock of the Observatory, and a break in the
transmission of the currents, once in every minute, namely, at
the sixtieth second, of the Observatory clock, supplies the
public with an unerring criterion for testing the accuracy of
the controlled clock. There were now eleven clocks of various
forms in Glasgow under the electric control of the mean -time
clock of the Observatory. In a short time the number would
be increased to some seventeen or eighteen, and the system
was gradually extending over all Glasgow. The going of
these clocks was truly marvellous. From week to week and
from month to month they continued to indicate the time with
the utmost precision, occasioning merely a little attention now
and then to the battery power. It was one of the advantages
of Jones's method of control that, even in the case wherein the
operations were on an extensive scale, only a small amount of
battery power was necessary. There was one other remark
which he would make, and it had reference to turret-clocks.
Hitherto it had been usual, in the operations for placing one
of such clocks under control, to remove the two seconds' pen-
dulum, and to substitute for it a seconds' pendulum, which was
made to beat in exact unison with the pendulum of the Ob'
servatory clock. Objections to this practice have been ex-
pressed by many persons who consider that a heavy pendulum
vibrating once in two seconds is much better adapted than a
light seconds' pendulum for maintaining the steady going of a
Digiti
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clock fitted up in a lofty tower, the dials and bands of which
are necessarily exposed very much to the action of high winds.
After a good deal of experiment, Professor Grant found that
the two seconds' pendulum might be retained and kept under
complete control by attaching a larger wire coil to the bob,
and using a more powerful system of magnets in combination
with it.
Mr. Fritchard : Do you mean that you control at once
pendulums that beat a second and pendulums that beat two
seconds by the same wire ?
Professor Grant : Yes. We have two turret-clocks in
which the long pendulum has been removed and the short one
substituted ; but we have a third one in which the long pen-
dulum has been retained, and the result has been completely
successful. Nothing can be more satisfactory. It goes on
from week to week without any trouble, and the result is as
exact as in the case of the smaller clocks.
Letter to the President from Dr. Donatio Director of the
Observatory^ Florence,
** Florence, le 27 Dec, 1865.
" Si Ton compare les elements, que j'ai calcule pour la
Com^te que le Rev. P. Secchi annon^a d'avoir trouvie le 9
courant, avec les elements de la Com^te de Faye, on s'aper9oit
que la Comete annoncee par le P. Secchi n'est autre chose que
la Comete de Faye.
"Peut-etre vous avez dejk fait cette remarque, que je
n'avais pas faite d'abord, en partie k cause de I'annonce donnee
par le Rev. P Secchi, et en partie parcequ'il ^tait r^ellement
peu presumable que dans ces jours on piit observer de nouveau
la Comete de Faye."
ERRATA.
Vol. XXV.. p. 56, end of line 13, and lines 15, 20, 23, and 25, and p. 57,
line 10, for a read 2«.
Vol. XXVT., No. I, page 34, line 11, for which surpassed, rea i that of Mr.
Rutherford surpassed.
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68
CONTENTS.
Pag«
Fellows elected 37
On the Determination of the Difference of Longitnde between the Ob-
servatories of Greenwich and Glasgow by Galvanic Signals, by
Prof. Grant ib.
On the Telescopic Disks of Stars, by Mr. Stone 45
On Personal Equation in Reading Microscopes, by Mr. Stone ... 48
Radiant Points of Shootbg-Stars, by Mr. Herschel 51
The November Meteoric Shower, by Mr. Glaisher 53
Observations of Occultations of Stars by the Moon, and Phenomena of
Jupiter's Satellites, made at Mr. Barclay's Observatory, Leyton,
N.E., by Mr. Talmagtf 57
Observations of the Comet III. i860, made at the Santiago Observa-
tory, Chili, by M. Moesta 58
Observations of Solar Eclipse, Oct. 19, 1865, by the Rev. T. Chevallier 60
Note on ^ Herctt/if, by Mr. Burr 61
Physical Constitution of the Sun, by Lieut. Ashe ib.
Letter firom M. Chacomac on the Physical Constitution of the Sun ... 62
Observations of Double Stars, by the Rev. Padre Secchl ib.
Photographs of the Moon, by Mr. Brothers ib.
Observations of Encke's Comet, by Mr. Smalley .. 63
Occultations of Stars by the Moon, observed at Forest Lodge, Mares-
field, by Capt. Noble ib.
Observations of the Solar Eclipse, Oct. 19, 1865, by Lord Wrottesley 64
Notice of a recent Memoir of Prof. Krueger, of Helsingfors, on the
Star-cluster in X Per«et, by Mr. Carrington 65
Account of the Time-signaHing Operations at Glasgow, by Prof. Grant 66
Letter to the President from Dr. Donati 67
Printed by STRUfozWATs and Waldek, Castle St. Leicester Bet., and Published
at the Apartments of the Society, January 13, 1806.
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MONTHLY NOTICES
OF THE
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVL January 12, 1866. No. 3.
Wareen De La Rue, Esq., President, in the Chair.
Thomas G. Rylands, Esq., Heath House, Warrington ;
Rev. A. W. Deej, Alton, Hants ;
Frederick Robert Hughes, Esq., Borrowstownness, N.B.;
The Hon. John William Strutt, Tirling Phice, Witham,
.Essex; and
Capt. Charles Thomas Curme, R.N., Milbome Port, Somer-
set,
were balloted for and duly elected Fellows of the Society.
Proposition for a Telescope on the Andes, By Lieut. E. D. Ashe,
Director of the Quebec Observatory.
{Letter to the President.)
As President of the Astronomical Society, I venture to
suggest to you that a first-class telescope should be placed on
one of the higher Llanos of the Andes, some of which are
admirably adapted for astronomical observations; and as the
Geographical Society has had no difficulty in raising funds for
several of their praiseworthy expeditions, neither do I anti-
cipate any difficulty in defraying the expenses of an astro-
nomical party, whose object would be to observe the discs of
planets and the surface of the Sun.
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70 Lieut, AshCy Proposition for a Telescope on the Andes.
Much was done bj the Tenerifie expedition ; still incom-
parably greater results might be expected from placing a glass
at a much higher elevation, and removed from the effects of a
moist atmosphere.
It was my good fortune, when belonging to a frigate on the
South American Station, to have crossed the Andes, in Peru,
in about Lat. 1 8° South.
The Pass of Tar cor a has an elevation of about 20,000 feet,
and is reached easily in three days from the delightful city of
Tacna, situated on the coast.
From the Pass to the Lake of Titicaca are numerous plains
or Llanos, at different heights, varying from 1 2,000 to 20,000
feet; one of which might be selected for the purpose. I
should be very happy to give any information or render any
assistance.
As a rough sketch of the route of the expedition to its
destination, I may say that the party should go by the West
Indian Mail to Panama ; there a man-of*war steamer would be
ready to take them to Arica, on the coast of Peru, and from
there the expedition would proceed to the pretty town of
Tacna, distant forty miles, where it could remain and enjoy
itself, and send out surveying parties, who would bring back
information, upon which it would select a spot^ and proceed to
its destination.
There would be no difficulty in conveying the different
parts of an Equatoreal, as a mule can carry 4 cwt. ; and as I
have seen a " CoUard and Collard '* pianoforte upon a mule's
back crossing the Andes, there can be no doubt that the dif-
ferent parts of the telescope could be carefully carried.
No one need join the party who could not stand a little
roughing, and endure the fatigue of thirteen hours upon the
back of a mule for several days together.
I enclose an account of my journey across the Andes, which
may give some information to those desiring to join the expe-
dition ; and, in conclusion, I may say that it is probable that
the Canadian Government would allow my telescope of 8 inches
aperture and my services upon so laudable an undertaking.
London f November 10, 1865.
The President : I have since received a letter from Com-
mander Ashe, and he very strongly urges the desirability of an
expedition to Peru. He has a very high opinion of the atmo-
sphere there, and thinks that we should obtain obseryations
such as we could get in no other part of the world. The letter
is of value, from its containing the experience of a man accus-
tomed to make astronomical observations.
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Mr. Huggins^ on the Stars within the Trapezium, S^c. 7 1
Mr. Evan Hopkins, who has travelled in Peru, bore testi-
mony to the excellence of the climate.
On the Stars within the Trapezium of the Nebula of Orion,
By William Huggins, Esq., F.B S.
Since a prismatic analysis of the light of the great Nebula
in Orion has shown that this remarkable object has a gaseous
constitution, the changes in the arrangement of the luminous
matter and in the relative brightness of different parts, which
some observers are of opinion are taking place in this nebula,
possess great interest and importance. For it will be probably
from a more careful and systematic observation of the altera-
tions in form and brightness which ma} take place in this
V
5
The Trapezium of Orion, as seen by Mr. Huggins,
Jan. 6 and ^, i266.
object, and in the other gaseous nebulae, that the necessary
evidence will be obtained for a future determination of the true
cosmical rank and relations of these bodies.
The discrepancy which exists between the published observ-
ations of the minute stars within the trapezium and in its
^neighbourhood, appears to show that the stains are subject to
considerable variation in brightness.
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72 Mr, HugginSy on the Stars within the
M. Otto Struve remarks, " We have amongst the six ob-
served stars in the Regio Huygheniana, on a space of three to
four square minutes, at least four variable stars ; but I think
the number of variable stars in the same region will yet be
considerably increased by further observations. The sixth
star of the trapezium bears strong indications of variability.
. . . Probably two or three stars, seen and measured by M.
Lamont in 1837, will be found of variable light. . • . Perhaps
some of the stars indicated by De Yico, Bond, and others, in
the immediate vicinity of the Trapezium, might be found of
variable light."*
On the evening of January 6, 1 866, the atmosphere was
unusually favourable for the detection of minute points of
light, and I was able to estimate satisfactorily the positions
and relative brightness of three very small stars situated within
the space enclosed by the well-known six stars of the Trape-
zium. They were detected with a Kellner eye-piece magni-
fying 60 diameters, and were afterwards seen with double-
convex lenses, magnifying 135 and 220 diameters. The observ-
ations of January 6 were confirmed on January 7 and 8.1
The positions of these minute stars relatively to the other stars
of the trapezium are shown in the diagram which accompanies
this paper.
The fifth and sixth stars were steadily seen. In 1852 Mr.
Lassell obtained some fine views of these stars, and he puts on
record that " the sixth star seemed equally bright with the
fifth, and quite as easily 8een.'*J On December 8, 1856, Mr.
Lassell remarks, " The sixth star appears decidedly the bright-
est, or the largest, intrinsically, and if in the place of the fifth
would I think be more easily seen. If these stars are unaltered
in magnitude I cannot understand why I should, many years
ago, have so often scrutinized the fifth star with this telescope
before I detected the sixth."§ In 1857 M. 0. Struve says,
" On former occasions I agreed perfectly with Mr. Lassell's
. remark that the sixth star was fully of equal brightness with
the fifth star ; but this year it appeared to me constantly in-
ferior."!
There appeared to me a considerable difference in bright-
ness between the fifth star and the sixth. Frequently during
the passage of masses of haze across the stars the fifth was seen
steadily when the sixth could not be detected. My observa-
tions agree with the magnitudes assigned to these stars by Sir
John Herschel in 1 834. Sir John Herschel says, "Applying the
aperture 12 inches, the sixth star was finely seen. It is ex-
* Monthly NoUcett vol. xvii. p. 227.
t On this evening my friend, Mr. S. B. Kincaid, visited the Observatory,
and saw all the stars figured in the diagram. *
X Monthly Notices, vol. ziv. p. 74. § Ibid. vol. zvii. p. 68.
11 Ibid. vol. xvii. p. 227.
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Trapezium of the Nebula of Orion, 73
cessivelj minute and very close to «, much more so than the
fifth is to y, sajhalf the distance, and 14th mag., while the fifth
= 1 2th mag."*
The minute star nearly in the middle of the Trapezium,
and marked 7 in the diagram, appeared to me much fainter
than the sixth star, probably nearly as much so as the sixth is
now smaller than the fifth. I do not know whether a star has
been seen before in this position within the Trapezium.
The star numbered 8 in the diagram is probably in a small
degree brighter than 7, but the nearness of 8 to the bright star
« makes the steady vision of it very difficult. This star can
scarcely be the same as the one which M. Porro saw in 1857.
In M. D'Abbadie's plan of the Trapezium, M. Porro's star is
placed nearly halfway from « to y.l
The star 9 of the diagram is rather feebler than 7. I was
able to see it only by occasional glimpses. I should think there
can be little doubt that this is one of the stars observed by De
Vice in i^zg*X I had recorded its place before I saw De Vico's
diagram. The position which I have given to it is not identi-
cal with that of De Vice's star, but the extreme difficulty of
this object made the determination of its position a little un-
certain.
No one of the minute stars which I observed agrees in
position with the "new star" discovered by Mr. Lassell at
Malta on January 29, 1862. A diagram of this star is given
in the Monthly Notices,^
We do not know whether these minute stars are physically
connected with the great nebula, or are only in optical associa-
tion with it. As a means of obtaining information on this
point, it appears to be of great importance to determine whe-
ther the variability of the stars in the nebula and the occa-
sional appearance of new stars can be associated with any
changes which may be observed in the nebula.
Captain Noble: My friend Mr. Brodie has informed me
that by gauging the fifth and sixth stars by Dawes's method of
diaphragms he has found that the sixth star was, on the night
he tried it, of precisely half a magnitude less than the fifth.
I have seen the sixth star with my 4^*^-inch aperture, and
therefore, from what Mr. Huggins says about variability, I think
the thing is put out of the range of hypothesis, and is almost
* Cape Observations, p. 30.
t Monthly Notices, vol. xvii. p. 245.-
I ** Memoria intomo a parecchie Osservazioni fatte in Collegio Romano,
anno 1839.'*
§ Vol. xzii. p. 164.
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74 Messrs. Warren De La Rue, Stewart^ and Loewy^
a certainty. I have tried many times to see that star, and
couhl not, and yet I have seen it at others: — the fifth I can
always see.
The President t I quite agree that the whole system of the
trapezium with the included faint stars is variable. At times I
have seen the sixth star very much brighter than the fifth,
Notwithstanding its proximity to its companion star, and I have
also caught sight of the fainter stars, stars within the trape-
zium, without noting down their positions at the time. I
believe those stars are variable because on other occasions I
have searched for them in vain, and I think this will be found
to be the ca?e. Whether one can establish a physical connection
between these various stars it is difficult to say, for some of
them are so extremely difficult to be seen, and their variabi-
lity renders it still more difficult to say whether it is the same
Star which is seen on different occasions. Diligent research and
observation with respect to the nebula of Orion will certainly
bring to light some interesting phenomena. I would also re-
commend the close observation of other groups of faint stars ;
for in many of these — I did observe them years ago more than
I do now-— I have noticed traces of variability.
Note regarding the Decrease of Actinic Effect near the Cir^
cumference of the Sun, as shown by the Kew Pictures, By
Messrs. Warren De La Rue, Stewart, and Loewy.
The remarks which we ventured to make in the last para-
graph of our Results on Solar Physics, recently published,
have induced us to examine the Kew Pictures, as regards the
decrease of actinic effiict from the centre to the circumference
of the Sun, to which decrease we may give the name of
atmospheric effect, since it is without doubt caused by the
presence of a comparatively cold solar atmosphere.
In conformity with our views, this atmospheric effect ought
to be greater at the epoch of maximum than at that of mini-
mum spot frequency ; and furthermore, if there is any refer-
ence to ecliptical longitudes in the behaviour of spots —
that is to say, if at any time the spots on the Sun attain their
maximum at any ecliptical longitude, there ought (according
to these views) to be a greater amount of absorbing atmo-*
sphere at the same longitude, since such an atmosphere is
supposed conducive to the outbreak of spots.
There is reason to think that spots attain their maximum in
the ecliptical longitude opposite to that where Venus exists, so
that we might expect (according to these views) a diminution
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Actinic Effect near the Circumference of the Sun. 7 5
in atmospheric effect in the same longitude as Venus, and an
increase in their effect in the longitude opposite to Venus.
If, therefore, Venus be at the longitude of the left limb of
the Sun, this limb should exhibit less atmospheric effect than
the right limb, and if Venus be at the right limb we should
have most atmospheric effect at the left limb.
It is only the under-exposed pictures that are available for
a research of this nature, since an over-exposure tends to do
awaj with the atmospheric effect.
Without giving any hint of our views, Mr. Beckly wag
requested to select some of the last Kew pictures taken in
1859, a year of maximum spot frequency, and to compare them
with those taken in 1 864 and 1 865, periods of minimum spot
frequency ; and he came to the conclusion that there was more
atmospheric effect in 1859 than in the years 1864 and 1865.
Furthermore, Mr. Stewart, in conjunction with Miss Beck-
ly, has looked over all the pictures taken at Kew from May
1 863 to the present date ; and this examination was made in
such a way that the results could not derive any bias from the
opinion of Mr. Stewart, as one of the joint authors of the
Researches on Solar Physics^ above alluded to $ for whenever
the two observers disagreed, the picture was referred to a third
person.
The results of this investigation are given in the following
table, and they are at least in conformity with our views, and
not antagonistic, while at the same time the evidence is not
sufficiently strong to establish conclusively the truth of an
hypothesis.
1863.
Left.
Bight.
Equal.
May
2
I
Venus from 80 to 20 degrees to the left
June
I
2
„ 50 to 60 „ „
July
7
2 .
„ 3oto4x> „ „
August
3
I ^
„ 10 to 20 „ „
September
2
Venus in conjunction.
October
2
Venus about 5-10° to the right.
November
3
„ „ 20® to the right.
December
2
I .
„ from 30° to 40° to the right.
1864.
January
\
„ about 45** to the right.
February
-
-
March
„ „ 90°
April
4
It 19 "o° M
xMay
•" >
Approaching opposition.
June
7 >
Very near opposition.
July
August
7
2
1 Venus in opposition.
September
2
About 150° to the left.
October
3^
„ 140^ „
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^6 Messrs. Warren De La Rue, Stewart^ and Loewy^
1865.
Left
Right.
Equal.
November
2
3>
About 120° to the left.
December
I
2
„ 90' .»
1865.
January
2
February
I
March
4
3
3>
April
2
II "
May
I
I
10
Venus in conjunction.
June
2
I
July
2
3
August
6
I
5 '
September
5
I
8
.
October
8
2
5
Venus 90° to the right
It thus appears, from the above table, which is the result
of a joint and careful investigation of the Kew pictures by
Miss Beckly and Mr. Stewart that
(i). When Venus is considerably to the left, there is most atmospheric
effect to the right.
(2). When she is in conjunction or opposition, there is a tendency to
equality.
(3). When she is considerably to the right, there is most atmospheric
effect to the left.
A Comparison of the Kew Results of Observations on Sun-
Spots with those of Hofrath Schwabe, in Dessau^ for the
year 1865. By Messrs. Warren De La Rue, Stewart, and
Loewy.
Kew. Dessau.
New
Months. Groups.
Days
Ob-
Nttmbers. served.
Days
without
Spots.
New
Groups.
Numbers.
Days
Ob-
served.
Days
without
Spots.
January
12
632 to 643
5
12
I to 12
^3
February
10
644 to 653
7
'(?)
II
13 to 23
16
March
10
654 to 663
16
i(?)
8
24 to 31
15
'(?)
April
8
664 to 671
15
12
32 to 43
30
May
13
672 to 684
19
2
10
44 to S3
31
June
685 to 689
10
i(?)
6
54 to 59
30
I
July
690 to 696
13
I
6
60 to 65
31
I
August
697 to 704
IS
7
66 to 72
31
September
705 to 711
22
2
7
73 to 79
30
7
October
712 to 714
»s
3
3
80 to 82
31
II
November
715 to 719
10
I
6
83 to 88
23
3
December
720 to 724
6
I
5
89 to 93
16
2
Total
93
632 to 724
153
Ih
93
I to 93
307
26
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Kew Results of Observations on Sun- Spots, yj
Remarks,— The numbers in the Kew list form a continuation of the Cata-
logue of Groups, published in the first series of Researches on Solar Physics,
by Warren De La Rue, Balfour Stewart, and Benjamin Loewy, pp. 6-8.
Those days on which it is doubtful whether spots were on the Sun or not,
have the sign (?) after them.
The President stated that the Kew photographs are now
taken by Miss Becklj, the daughter of the mechanical assist-
ant of Kew; and it seems to be a work peculiarly fitting
to a lady. During the day she watches for opportunities for
photographing the Sun with that patience for which the sex
is distinguished, and she never lets an opportunity escape
her. It is extraordinary that even on very cloudy days, be-
tween gaps of cloud, when it would be imagined that it was
almost impossible to get a photograph, yet there is always a
record at Kew.
Mr. De La Rue remarked that all these investigations on
the solar spots occupy a considerable time, and that the results
may be interpreted differently by different persons. All that
we have to do is to record faithfully the result of our ob-
servations; and it is hoped the Kew photo-heliograph will
conduce very much to the advance of solar physics. Some
time ago some experiments were made by the speaker, in
taking solar spots on a very large scale, the pictures of the
Sun's disk being on a scale of 3 feet for the Sun's diameter.
There are certain difficulties in taking those pictures by means
of a reflector ; but Mr. Cooke has recently undertaken the con-
struction of a 1 3 -inch refractor, which it is intended to apply
tx) solar and lunar photography.
On a New Method of Mounting Silvered Glass Specula and
Diagonal Mirrors in Reflecting Telescopes, By John
Browning, Esq., F.R.A.S.
Owing to their cheapness and portability, telescopes con-
structed with Foucault's silvered-glass mirrors are receiving a
constantly increasing share of attention.
The focal length of these mirrors needs not exceed eight
times their diameter, while for each inch in diameter — when of
the best figure — they will bear a magnifying power of 100 on
close stars in finest states of air.
The principal difficulty hitherto encountered in fitting-up
these mirrors, when they are of large size, has been that of
mounting them in such a manner as to avoid flexure. Various
contrivances have been employed for this purpose ; among
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78 Mr, Browning y on a New Method of Mounting
others they have been supported on air-cushions, on layers of
felt, and on a number of triangles, each triangle supported on
a centre. All these plans appear to me to possess the common
fault, that a blow, or shock of any kind, or even a change in
the position of the telescope, frequently throws the speculum
out of adjustment. The method I have devised for overcoming
this difficulty I shall now proceed to describe.
First, however, I wish to state that I have the mirrors
made of glass much thicker than is generally employed for the
purpose. For a speculum 6f inches in diameter I use glass
of a thickness of i inch, for a speculum lo inches in diameter
glass I J inches in thickness. The extra cost of the glass, as
it is only ordinary plate-glass, is merely nominal, and the diffi-
culty of working the mirror not at all increased.
After the disk which is to form the mirror is shaped, but
before the parabolic figure has been given to it, I work the
back carefully to a very perfect plane, by the same method I
employ for working the plane surfaces of prisms. When this
has been done the mirror has the parabolic figure given to it.
Fig. I.
A cast-iron cell (B, fig. i) is now prepared, whose internal
diameter is rather larger than the mirror. The bottom of this
cell when intended for a lo-inch mirror should be at least
three-quarters of an inch thick.
The inside of this cell, on which the mirror will have to
rest, I also bring carefully to a plane surface in the following
manner. I first turn it with a slide rest in a lathe in the usual
way. Then I prepare a Whitworth's plane surface of a circu-
lar form, one- eighth of an inch less in diameter than the mirror
to be mounted. The bottom of the cell is made flat by scrap-
ing, being tested repeatedly during the process with the circu-
lar Whitworth's surface.
It greatly facilitates this operation if a grove be turned m
the bottom of the cell, at F F, in diagram i . The centre of the
bearing surface of the cell, to the extent of one-third, may be
advantageously turned away. This materially lessens the risk
of the mirror being deflected, either by the presence of any
particles of foreign matter or by the cell altering its form
owing to changes of temperature.
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Silvered Glass Specula and Diagonal Mirrors, 79
For this suggestion I am indebted to the kindness of Colonel
Strange. Before the mirror is placed in its cell, the bearing
fiurface is slightly smeared with the best oil, to prevent the
oxidation of the iron. Lastly, the mirror is secared in its
position by a ring shown at G 6 in diagram i.
In adjusting the mirror it is necessary to avoid placing
any strain upon the cell, as a very small strain is sufficient to
dei9ect the bottom of the cell, and this deflection extends to
the mirror. This is avoided by placing the cell in another cell,
and adjusting it in position by means of hollow screws, D D, E E,
as shown in the diagram. These screws allow of the cell being
raised or lowered without throwing any strain upon the cell.
The silvered surface of the mirror is protected by a tightly-
fitting cover, which is adapted to the edge of the cell, B, which
is turned conical.
Some time since Mr. With, of Hereford, so well known for
the success with which he has given his attention to the con-
struction of silveredoglass specula, suggested to me that their
performance would probably be improved if some other method
were adopted of mounting the diagonal reflector or prism.
As at present mounted on an arm, they are subject to
vibration, and the substance of this arm produces coarse rays
on bright stars.
I have endeavoured to obviate these inconveniences by the
plan of mounting represented in the diagrams figs. 2 and 3.
In these diagrams fig. 3 is a perspective drawing, and &g, 2 a
front view of the arrangement.
The letters are the same for the same parts in both dia-
grams. D represents the diagonal mirror ; B B B, three pieces
of chronometer spring stretched tightly, by means of screws
through the ring, AAA. This movement is available for
centreing. The diagonal mirror or prism, D, is attached by
three pillars to a round plate, E, whose diameter is the minor
axis of the ellipse. The adjustment is made by means of
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8o Mr, Broioningf on a New Method of Mounting
hollow screws, of the same kind I haive referred to in the com-
mencement of this paper, as applied to the speculum.
The most difficult tests for silvered-glass specula are very
bright stars of large magnitude. Their performance on this
class of objects is considerably improved by using a good
Barlow lens of 4 or 5 inches virtual focus. At the same time,
as is well known, the employment of this lens forms a most
convenient contrivance for increasing the power of the various
eye-pieces. For low powers, achromatic eye-pieces made by
combining two achromatic combinations, each consisting of a
plano-concave flint and a double-convex crown cemented toge-
ther, arranged so that the convex side of the crown lenses
almost touch each other, answer well. When used in this
manner, if the parabolizing operation on the speculum has
been conducted with sufficient care and skill, the performance
of an 8 J -inch speculum will bear favourable comparison with
a 7-inch refractor in point of light, and exceed it in separat-
ing power, while the expense need not be more than one-fifth
of the cost of such an object-glass.
In conjunction with Mr. Slack, I have contrived a simple
and very substantial form of equatorial mounting entirely in
cast-iron for these telescopes. At the same time I am greatly
indebted to Mr. Slack for the valuable assistance he has ren«
dered me in carefully testing the results of the various modifi-
cations I tried in the course of my experiments on mounting
specula, before I finally adopted the plans I have just described.
With a plain glass mirror as a diagonal reflector, unsilvered,
so as to allow the heat-rays to pass freely, these telescopes
answer admirably for observations on sun-spots.
Telescopes provided with these mirrors are well adapted
for spectrum observations on the stars. From their large
aperture, as compared with their focal length, they give abun-
dance of light, and they are not liable to any disadvantages on
the score of the want of achromacy.
It is well known there is a considerable number of inter-
esting observations which can only be made with large aper-
tures, and that consideration of expense alone has hitherto
prevented their being used.
A damp atmosphere is very prejudicial to the silvered sur-
face of these specula. I have endeavoured to obviate this
difficulty, and at the same time prevent the spiral-tube currents
by covering the mouth of the telescope with a disk of glass,
having plane and parallel surfaces. The production of these
parallel plates is attended with considerable difficulty, but I
have succeeded in applying one of 8-inches diameter to a
mirror, apparently without injuring its performance, but I
regret that I cannot speak upon the subject with confidence,
as the long continuance of unfavourable weather has prevented
me from making any satisfactory experiments.
I shall be highly gratified if. the attention I have given to
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Silvered Glass Specula and Diagonal Mirrors, 8i
the mountiDg of these mirrors and telescopes should lead to
their more general adoption.
The President: I think the most important part of the
communication is the means of suspending the small mirror.
The suppression of a great part of the thickness of the
arm tends to do away with the rays which we all know appear
to shoot out from the image of a star in the reflector. With
respect to the mounting of the large mirror, I think that Mr.
3rowning's plan would answer very well up to 6 or 8 inches,
but the moment one goes beyond that size there must be some
such means of suspension as that adopted in Mr. Lassell's
telescopes, or there must be flexure ; no accuracy of fitting
will prevent that.
Observations and Elements of the Comet of December 9, 1865.
By Prof, Donati.
(Tratulation qfa Letter to the President.)
I have determined the following positions of the Comet
discovered by the Rev. Padre Secchi at Rome on the 9th
December : —
Florence BLT.
B.A.
Decl.
186fi.
h m 8
h m 8
/ «
Dec. II
7 9 >9
22 50 I 8*44
+ 4 15-9
12
6 44 20
22 52 12*55
3 56 43-8
»3
8 II 30
22 54 I 6*70
3 5» 5'3
H
8 16 20
22 56 14-72
3 47 36-5
15
8 16 46
22 58 13-90
3 43 12-2
16
8 23 49
23 14-74
3 38 26-9
»7
8 52 34
23 2 17*89
3 33 i6-o
18
8 28 40
23 4 17-19
3 28 13-2
19
8 9 28
23 6 15-84
3 22 53-1
so
8 14 47
23 10 28*20
3 17 ii-i
21
8 18 58
23 10 28-20
+ 3 " «'5
The Comet is of extraordinary faintness. Using the ob-
servation at Rome of the 9th December, and my own ob-
servations of January 13 and 19, I have calculated the fol-
lowing elements : —
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82 Mr, Talmage, Occultation of \i^ Tauri by the Moon,
T « 1866, Jan. 20-32064 Greenwich M.T,
9> = 205 15 39I
«* = 31 22 31 I' Mean Equinox, 13 Dec. 1865.
t » 12 14 loj
log. q = 0-28886
This orbit satisfies exactly the mean observation, but it
gives for the observation of Dec. 21 the following errors \^
0l«.-C4l.
B.A. Decl.
23**7 +8''9
Although the elements are only a rough approximation,
we see that the orbit is quite different from that of the Comet
of Biela, especially in the perihelion distance and in the
position of the orbit in its plane. But the new Comet
moves in a plane not veiy different from that of the Comet of
Biela, and passes its perihelion nearly at the same time.
These coincidences and the circumstance of not finding tlie
Comet of Biela at its place may be the result of accident, or
may have a physical reason. It seems to me that the mys-
terious phenomena which have been already remarked in
Biela's Comet permit the asking of this question — which at
present I cannot answer; but it may be hoped that science will
give a solution of it.
Florence, 22 Dec* 1865.
Occultation of 11^ Tauri by the Moon.
By C. G. Talmage, Esq.
I bog to enclose the times of the occultation of 115
Tauri on 1865, December 30:-—
h m 8
O.M.T. of Diaappeanance = Dec. 30 7 34 55*60
tt Reappearance t 21 54*35
Both times are exact, observed with a power of 85 on the
10-inch Equatoreal.
Mr. Barclay*s Observatory^ Lei/ion,
1866, January 11.
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Mr. Tebhutty ObservaHoTis of a Argus. 83
Observations of% Argus. B7 J. Tebbutt» Jun. Esq.
In accordance with the promise contained in my letter of
the 17th July last, I now send you mj observations of the
remarkable southern star « Argus. The comparisons have all
been made with the naked eye, unless where otherwise stated,
and under the most favourable conditions of sky, &c. The
first comparisons were made in July 1854; but it appears from
my journal that n Argus was employed by me as a comparison-
star on the 30th September and 12th October, 1853, in sextant
observations of a large oomet at that time visible in the morning
sky. It was then a reddish star of the first magnitude.
1854, July 5. Of « and /3 Centauri, « Crucis, and n Argus,
the first was by far the brightest ; /3 Centauri and « Argus
were very nearly equal, but I think the latter was somewhat
the brighter, n Argus somewhat exceeded « Crucis.
1 860, May 4. 8 p.m. n Argus was less than fi Canis Ma^
joris and about equal to /3 Canis Minoris. The standard stars
were, however, too near the horizon for a good comparison, and
the Moon was very bright. It was also about equal to i Cruets
and ^ Argus.
1 860, May 1 8. 6'' 30" p.m. About equal to ^ Canis Mi^
noris, but not quite so bright as fi Canis Majoris.
1862, January 26. Not so bright as ^ Canis Minoris or
$ Argus; perhaps slightly less than c Orionis, and exactly
equal to B.A.C. 3740.
1862, June 23. About equal to i Crueis and B.A.C. 3526
and 3619, and considerably less than ) Crueis or $ Argus.
1862, July 1 9. Greater than B.A.C. 3688 and less than
B.A.C. 3740. The same result was obtained with a small
telescope.
1862, July 22. D Argus was of a magnitude intermediate
between B.A.C. 3740 and 3688, and very little brighter than
5 and n Crueis.
1862, July 24. 9**' 23"*. Slightly less than B.A.C. 3740
and 1 81 8, and exactly equal to B.A.C 3594.
1862, July 25. 6'* P.M. Less than B.A.C. 3740 and 3818,
equal to B.A.C. 3594, and greater than B.A.C. 3695 and 3688.
1 862, August 28. 7*» 20™ P.M. Greater than B.A.C. 3688 ;
equal to B.A.C. 3594; and less than B.A.C. 3740.
1863, April 15. \o^ P.M. Greater than B.A.C. 3655 and
3688, and less than i Crueis and B.A.C. 3740 and 3818. It
was decidedly a shade less brilliant than B.A.C. 3594.
1863, April 16. II P.M. Somewhat less than «' and «*
Scorpii and B.A.C. 3594.
1 863, May 24. 8** 1 5™ p.m. Less than g Crueis and B.A.C.
3740 and 3818 ; greater than B.A.C. 3688 ; and about equal to
Digiti
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84 Mr. Tehhutty Elements of Comet I. 1865.
o»^ and M^ Scorpiu It was decidedly a shade less brilliant than
B.A.C. 3594, which was very nearly equal to B.A.C. 3818.
1864, March 23. 9^ p.m. Equal to B.A.C. 3655 and 3688,
both by the naked eye and the telescope. Full Moon.
1864, April 23. 6*» 30" P.M. A shade less than B.A.C.
3655 and 3688 ; it was certainly not greater. It was brighter
than B.A^C. 3642, which could only be seen by oblique vision.
1864, May 31. 7** P.M. About equal to B.A.C. 5501, a
small star a little north of Antares, and about equal to or
perhaps slightly inferior to B.A.C, 3655 and 3688; it was
superior to B.A.C. 3642.
1864, July 28. 7** P.M. Somewhat inferior to B.A.C. 3655
and 3688, and slightly superior to B.A.C. 3642.
1 865, February 22, 23, and 24. 9** p.m. h Argus was cer-
tainly inferior to B.A.C. 3655 and 3688 ; the stars were at a
great altitude.
1865, March 14. 9** 20° p.m. m Argus was distinctly vi-
sible to the naked eye, notwithstanding the Moon. It was
certainly not quite so bright as B.A.C. 3655 or 3688.
Windsor^ New South Wale»,
October 19, 1865.
Elements of Comet I. 1 865. By J. Tebbutt, jun. Esq.
I also avail myself of this opportunity to forward my
corrected elements of the Great Comet of this year; they agree
pretty well with the series of observations made at Melbourne
and Windsor.
T = 1865, January h*' 32510 G.M.T.
o t
» 4 50 »4-4| M. Equinox, 1865-0.
SI a53 3 io'4'
t 92 28 20*0
log q = 8*4i4756i
Windsor^ New South WaleSy
October 19, 1865.
Digiti
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M. Delaunay^ on the Secular Acceleration^ 4*c. 85
There is contained in the Comptes Rendus of the French
Academy, t. Ixi. (December 1865), an interesting paper by
M. Delaunay — " Sur TExistence d'une Cause NouveUe ayant une
influence sensible sur la valeur de Tequation seculaire de la
Lune." The substance of this paper is as follows : —
Assuming that the secular acceleration of the mean mo-
tion of the Moon, as indicated by observation, is notably
greater than that occasioned by the variation of the excentri-
city of the Earth's orbit, it becomes necessary to seek for a new
cause for the excess in question, or portion not accounted for
by Laplace's theory. A progressive cooling of the terrestrial
globe would produce a diminution, not an increase, of the ac-
celeration, and the effect is therefore not to be so accounted for.
But M. Delaunay considers that he has found a cause to which
it is natural to attribute the excess in question, a cause, that
is, which produces a progressive retardation in the rotatory
motion of the Earth, and consequently an apparent accelera-
tion in the mean motion of the Moon.
We know that the Moon by its action on the waters of the
ocean occasions therein an oscillatory motion constituting the
phenomenon of the tides. The Sun concurs in the production
of this phenomenon, but, to avoid complication, the solar action
may be disregarded. The form of the surface of the sea chang-
ing continually, it follows that the action of the Moon on the
entire mass of the Earth (including therein the waters of the
sea) is at every instant somewhat different from what it would
be if the phenomenon of the tides did not exist ; in seeking to
explain wherein consists the difference, it is seen that it con-
sists principally in a couple acting constantly on the Earth
in a direction contrary to the rotatory motion, and that the
result is a progressive diminution of the angular velocity of the
terrestrial globe.
To further explain this, imagine, in the first instance, that
the Earth is entirely covered by the waters of the ocean. In
virtue of the action of the Moon, the waters tend to elevate
themselves above their mean level in the two opposite regions
situate at the extremities of the diameter directed towards the
centre of the Moon. Admitting for greater simplicity that,
without this action of the Moon, the surface of the sea would
be exactly spherical, and that the Moon is in the plane of the
Equator, then, in virtue of the lunar action, the surface of the
sea tends constantly to assume the form of an ellipsoid of re-
volution, having the same centre as the sphere, and its trans-
verse axis directed in the line joining the centres of the Earth
and Moon. The effect of the Earth's motion of rotation is that
this ellipsoid moves in regard to the Earth exactly as the
Moon in its diurnal revolution, since the axis of the ellipsoid
is always directed towards the Moon. But this continual dis-
Digiti
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86 M. Delaunay, on the Secular Acceleration of the
placement causes that the surface of the waters is never coin-
cident with that of the ellipsoid of equilibrium — the frictions
and resistances which the waters suffer in their motion produce
the effect that the axis of the elongated figure of the waters at
any instant lags behind that of the ellipsoid of equilibrium
wherewith it tends to coincide. Without this retardation, the
high tide would take place at the instant of the passage, supe-
rior or inferior, of the Moon over the meridian ; in consequence
of the retardation, the high tide takes place, not at the instant
of the passage, but some hours after it.
The phenomenon is more complicated in the actual case,
where the terrestrial surface is not completely covered by the
waters, but whatever the distribution of land and water may
be, the frictions and resistances of every kind which the waters
suffer in their motion produce an effect similar to that indi-
cated in the first-mentioned case. There is always a retarda-
tion in the oscillatory movement. Speaking generally, the
oscillatory movement is what it would be if these resistances
did not exist, and if the Moon was at every instant in a posi-
tion in the heaven behind the actual position, in regard to the
direction of the apparent diurnal motion.
Returning to the more simple case where the surface is
completely covered, let us consider how the action of the Moon
is modified in consequence of the elongated form produced in
the waters of the sea by this same action. There exist, as it
were, two fluid prominences, situate at the extremities of a
diameter directed, not towards the Moon itself, but towards a
point in the heavens situate at a certain distance eastwardly
from the Moon. These two prominences are at unequal dis-
tances from the Moon, the one nearer, the other further
than the centre of the Earth. Bearing in mini the explana-
tion of the lunar action which produces the tides, it is easy to
see that the nearer prominence is, as it were, attracted to, the
further prominence repelled by, the Moon. The resultant ac-
tion is that of a couple applied to the mass of the Earth, and
tending to make it rotate in the direction contrary to that of
its actual motion — a couple which therefore tends to retard the
motion of rotation.
M. Delaunay remarks in a note that this idea of the resist-
ance which the Moon continually opposes to the rotatory motion
of the Earth, in consequence of its action on the waters of the
sea, has been referred to in several printed works ; but that it
has been always assumed that the effect is too small to be
sensible. He recalls that the object of his communication to
the Academy was not to make known this cause of retardation,
but to show — I. That the resulting retardation is far from
insensible; 2. That it is possible to see therein a complete ex-
planation of the portion, not accounted for by Laplace's theory,
of the lunar acceleration.
Returning to the discussion, and imagining to fix the ideas
Digiti
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Mean Motion of the Moon. 87
that the retardation of the time of high water is three hours,
or, what is the same thing, that the diameter through the two
prominences is inclined at an angle of 45^ to the line directed
to the centre of the Moon, let us calculate the effect which the
couple produces, replacing the two liquid prominences by ma-
terial points situate at the extremities of the oblique diameter
in question.
Denoting by T the centre of the Earth ; by L that of the
Moon ; by E the extremity of the equatoreal radius inclined at
an angle of 45° to the line T L eastwardly ; and by E' the
opposite extremity of this diameter ; let M be the total mass,
m the mass of the Moon, and (a that of each of the material
points supposed to be placed at E and E' respectively. Sup-
pose moreover that R is the distance TL, taken to be con-
stant, of the centres of the Earth and Moon, t the terrestrial
radius TE or TE'; and d the distance of the centre of the
Moon from the point E. Taking / as the unit of attraction,
we have
for the attraction of the Moon on the material point of mass fc
at E. To refer the motion of the terrestrial globe to axes
fixed in direction through its centre of gravity, we must join
to this a force "^^^ acting along the line L T in the direction
from L to T. We have, moreover,
<r =* R* + r« - 2 Rr cos 45** = R« + r* — \/2 Rr.
The resultant of these two forces constitutes the relative
action of the Moon on the mass |«* at E: taking the sum of
these moments in regard to the centre of the Earth, and neg-
lecting smaller terms, we find - ^^^ > ^^^ *^® expression of
the moment in question.
The same expression gives also the moment in regard to
the second mass (a at E'. The total moment produced by the
attractions on the two masses /b6 at E and E', tending to retard
the motion of rotation, is therefore equal to !^f ^ , and con-
sequently the differential equation for the motion of rotation,
M being the angular velocity and I the moment of inertia of
the Earth in regard to a diameter, is
dtit zfmfAT^
dt ^ r^~'
and taking the Earth to be homogeneous, we have
Digitized by VjOOQIC
88 M. Delaunay^ on the Secular Acceleration of the
I =-Mr».
Moreover, by considering the motion of the Moon about
the Earth, and disregarding (a in comparison of M, we find
f = ^ , where T is the period of the sidereal revolution of
the Moon about the Earth. Introducing the values of I and/,
the differential equation becomes
dm ^ m fA
and, integrating twice, it appears that the total angle of rota-
tion during the time t is, in consequence of this action of the
Moon, less than it would otherwise be by a quantity A, the
expression of which is
^tn fit i*
Let us now inquire what is the value to be attributed to
these masses /t6, in order that the retardation A corresponding
to a time t equal to a century, may give rise to an apparent
acceleration equal to 6 seconds (which is about the value of the
portion not accounted for by Laplace's theory). We must for
this purpose suppose A equal to the angle described by the
Earth in its rotatory motion, while the Moon advances 6
seconds in its mean motion round the Earth ; A is therefore
equal to 6 seconds multiplied by 27^ or to 164 seconds.
Effecting the calculation, and taking — for the ratio of the
Moon's mass to that of the Earth, we find
u = : M.
4160000000
To gain a more distinct notion of the magnitude of this
mass, assume that it is the mass of a volume V of water ; then,
if 5,5 is the mean density of the Earth, we find
V = 1429 000 000 000 cubic metres,
or, if this mass of water of the volume V has the form of a
stratum on a circular base of the uniform thickness of one
metre, the radius of the base will be about 675 kilometers;
that is to say, such a stratum applied to the surface of the
Earth would occupy a breadth of about 12 degrees at the
equator : the magnitude of this stratum of water is obviously
Digiti
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Mean Motion of the Moon. 89
comparable with those of the fluid prominences which the
action of the Moon would produce in the hypothetical case in
question*
In presence of the foregoing result, obtained, indeed, on an
hypothesis very different from the actual circumstances, it is,
as M. Delaunay considers, impossible not to admit that an ana-
logous effect of a sensible magnitude is produced by the Moon
on the waters of the ocean.
The Sun, which contributes to produce the phenomenon of
the tides, though in a less degree than the Moon, should equaUy
contribute to this progressive diminution of the rotatory motion
of the Earth.
The author states as follows his general conclusion : —
The perturbing forces to which are due the periodic oscil-
lations of the surface of the sea (phenomenon of the tides) in
exercising their action on the fluid intumescences which they
occasion, cause a progressive retardation of the movement of
rotation of the Earth, and thus produce a sensible apparent ac-
celeration in the mean motion of the Moon.
He remarks that the foregoing result is not in accordance
with what Laplace has found in investigating the influence
that the state of fluidity of the waters of the sea may have on
the movement of the terrestrial globe considered as a whole.
Laplace says formally that this state of fluidity of the sea does;
not affect the uniformity of the rotation of the globe {Meca"
nique Celeste, book v.) But it is to be remarked that to arrive
at this conclusion, Laplace confines himself to quantities of the
first order in regard to the perturbing forces considered by
him. It was, therefore, impossible for him to find the retard-
ation of the movement of rotation, the real existence whereof
has just been established, since this retardation is evidently of
the order of the square of the perturbing forces in question.
The exact calculation of the retardation due to the com-
bined action of the Moon and Sun, would require a knowledge
of all the circumstances of the tides as well along the shores as
in mid-ocean. Such a direct calculation is impossible; the
actual retardation can only be found indirectly by means of
the lunar acceleration, as determined by observation ; and this
gives a new interest to the comparisons of the lunar tables with
the ancient eclipses, in the view of thereby arriving at the true
value of the lunar acceleration.
The President called attention to two very important
works among the presents; one from Professor Hansen and
the other from M. Delaunay.* The volume contributed by Pro-
* The above-mentioned memoir in the Comptes Rendus. — Ed.
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90 On the Secular Acceleration of the
fessor Hansen relates to the Lunar Theory, and is the second
volume of the important work undertaken by that distinguished
physical astronomer. This volume will afford an opportunity
of studying the theory of Hansen with regard to certain
inequalities of the lunar motion, and of comparing his investi-
gation of the lunar acceleration with that of Mr. Adams. The
coefficient of the lunar acceleration obtained by Prof. Hansen
is much higher — about double that obtained by Mr. Adams ;
and a short time back there was a great controversy on the
subject of the correctness of the one or the other. However,
it seems to be established that Mr. Adams' coefficient is cor-
rect ; but there can be no question that it does not fit exactly
with the records of the ancient eclipses. M. Delaunay now
steps in opportunely and proposes to account for this differ-
ence by the assumption that there is a retardation of the
period of rotation of the Earth produced by the action of the
Moon on the waters of the Earth, and causing the Earth to
rotate more slowly by about looth of a second than it did
2000 years ago. Whether the hypothesis will or not be at
once accepted as true, it is certain that everything which
comes from M. Delaunay must be regarded with the highest
respect.
Mr. Stone said as follows : — The question discussed by M.
Delaunay in this paper is a most interesting and important
on. To clear up my own ideas on the subject, I have tried the
question in a slightly modified, but, I believe, in a strictly
analogous form. Suppose the Earth a sphere; the Moon to
move in the plane of the equator ; the Earth surrounded by a
small solid shell of the mean density of the sea; the outer
surface of this shell to assume the form of a prolate spheroid.
Then, if the shell moves in such a manner that its greatest
axis always lags three hours behind the Moon, the same
assumption as that made by M. Delaunay, we have a
rough geometrical representation of the " lunar tides." The
shell can only move in this constrained manner through the
action of friction between the shell and the Earth. I have
first determined the moment of friction required to produce the
constrained motion of the shell, and then the dimensions of the
shell required to produce a diminution in the Earth's velocity
of rotation, such that from it there would result an apparent
acceleration of 6'^ in the Moon's mean motion. I find that a
high tide of only 2 inches would be sufficient to produce the
required retardation of the Earth's velocity of rotation. My
result closely agrees with M. Delaunay's ; my mass is even
larger than his. This is as it should be, from the distri-
bution of the mass in my problem. I would, however, remark
that the case here considered is essentially that of a solid shell.
Every particle of this shell has to move around the Earth in
each month. I fear that the motion of a fiuid mass under like
conditions would be so exceedingly different that it would be
Digiti
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Mean Motion of the Moon. 91
very difficult, if not impossible, to infer anything like quanti-
tative results respecting the fluid case from the solid case of
our problem. I cannot think that any mere comparison of the
matter in the protuberant parts of the solid spheroid and fliud
spheroid gives us sufficient information on this point. No
doubt, when pushed to the second order of small quantities,
and therefore in an accurate solution, some retarding effect
would be produced in the case of a fluid mass moving with high
water lagging behind the Moon. The mean positions of the
oscillating particles of fluid would be bodily transferred. We
should have for the relative velocities of the fluid mass per-
pendicular to the Earth's axes non-periodic terms, and from
such terms there would arise a permanent frictional moment
on the Earth tending to destroy its velocity of rotation ; but
the question is, to what extent would this be the case. I
cannot see that M. Delaunay's paper gives us any information
on this point. I cannot therefore accept it as a demonstration
of a retardation of the Earth's rotation sufficient to produce
sensible effects on the apparent secular acceleration of the
Moon.- Whether the action of the friction between the Earth
and the sea, necessary to produce the observed retardation of
the tides, does produce a sensible eflect on the length of the
day or not, will, I fear, have, for the present, to be decided by
the agreement or non-agreement of the theoretical value of the
secular acceleration of the Moon's mean motion calculated on
the assumption of the invariability of the sidereal day, with
the observed value. Whether we accept or not the results
of M. Delaunay's paper, there can be no difference of opinion
respecting its value in recalling attention to the effects of the
phenomena of the tides on the Earth's rotation.
Instrument for Sale,
Achromatic Refi*actor, 6^-inch aperture, 8 J -feet focal
length, with complete equatoreal mounting, driven by clock-
work. Mounting by Troughton & Simms; object-glass by
Merz. Apply to the Assistant Secretary.
Digiti
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92
CONTENTS.
Page
Fellows elected , 69
Propositioii for a Telescope on the A.ndes, by Lieut. Ashe . . . . ib.
On the Stars within the Trapezium of the Nebula of Orion, by Mr.
Huggins 71
Notes regarding the Decrease of Actinic Effect near the Circumference
of the Sun, as shown by the Kew Pictures, by Messrs. De La Rue,
Stewart, and Loewy . . . . . . . . . . . . . • 74
A comparison of the Kew Results of Observations on Sun- Spots with
those of Holfrath Schwabe, in Dessau, for the year 1865, by
Messrs. De La Rue, Stewart, and Loewy 76
On a New Method of Mounting Silvered Glass Specula and Diagonal
Mirrors in Reflecting Telescopes, by Mr. Browning . . . . 77
Observations and Elements of the Comet of December 9, 1865, by
Prof. Donati 81
Occultation of 115 Tauri by the Moon, by Mr. Talmage . . . . 8a
Observations of n ArgUa, by Mr. Tebbutt 83
Elements of Comet I. 1865, by Mr. Tebbutt 84
M. Delaunay's Memoir on the Secular Acceleration of the Mean
Motion of the Moon . . . . . . . . . . . . . . 85
Instrument for Sale . . . . 91
Printed by Strangeways and Waldek, Castle St. Leicester Sq. and Published
at the Apartments of the Society, Feb. 8. 1866.
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MONTHLY NOTICES
OF THB
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVI. February 9, 1866. No. 4.
Thk Annaal General Meeting of the Society :
Warren De La Rue, Esq., F.B.S., President, in the Chair.
Arthur Brewin, Esq., 2 Copthall Chambers ; and
Arthur Finch, Esq., Roupell Park, Streatham Hill,
were balloted for and duly elected Fellows of the Society.
The President then said : —
Before proceeding with the business before us, I would,
for a few moments, bespeak your attention. You will recall the
great regret felt by us all on learning that the Medal awarded
last year to Professor Bond, of the United States, did not reach
that country until after his lamented decease.
You will, doubtless, therefore, be much gratified now to
learn that Professor Bond, though he did not actually receive
the Medal, was, some time before his death, made aware of the
honour that had been conferred upon him, and even of the
grounds on which the award had been made. For, being very
desirous of not omitting the mention of any of his numerous
works, I early in January transmitted to him a rough copy of
my intended address, with a request that he would kindly
point out any omissions. Although himself too ill to reply,
he, by his friend Lieut. Safibrd, expressed his heartfelt grati-
fication at this recognition of his labours, while at the same time
he confirmed the general accuracy and completeness of my
proposed account of his researches.
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94
Report of the Council
Report of the Council to the Forty-sixth Annual General
Meeting of the Society,
Progress and present state of the Society: —
1
"^1
^
•0
of a
£
1
December 31, 1864
163
264
14
5
456
49
505
Since elected
Deceased
Name withdrawn
ExpeUed
Resigned
Removals
7
-5
2
22
—2
— 2
— I
-3
Dec. 31, 1865
167
272
22
4
465
46
5"
Treasurer's Report of Receipts and Expenditure for the
year ending December 31, 1865: —
RECEIPTS.
Balance of last year's account
£
8.
d.
£
281
10
<2.
II
By Dividend on ^2100 Consols
30
H
3
By ditto on ^^4700 New 3 per Ctents
68
H
9
By ditto on j^2 100 Consols
30
19
6
By ditto on ^^5000 New 3 per Cents
73
>S
6
On account of arrears of contributions . . .
H7
16
3
164 contributions, 1865-6, 6-7
343
7
9 compositions
189
29 admission-fees
60
18
2 1 first contributions
34
13
Sale of publications
...
.
,
775
73
>4
13
Due to Assistant- Secretary — petty cash
...
■
£
I
I
1335
2
6
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to the Farty-sixth Annual General Meeting. 95
EXPENDITURE.
Salaries:— £ *. d. £ s. d.
Editor of Publications 60 o o
Assistant Secretary 100 o o
Commission on Collecting 33 o o
Inyestments : —
Purchase of £300 New 3 per Cents, 86| 266 12 6
Ditto ;^200 Consols, 89 j: ... 178 15 o
Taxes :—
Assessed and Income 823
Parish Rates 13 10 10
Bills: —
Strangeways and Co., printers
206 3
4
J. Ramfitt, bookbinder
2 19
8
J. Basire, engraver
4 8
9
Pearson, wood engraver
I 7
Tumor Fund
4 7
3
Annual Dinner
7 6
Law expenses
60
Insurance
10
6
Miscellaneous items : —
Books and parcels
4 19
I
Postages
34 15
2
House expenses
22 18
8
Expenses of evening meetings
13 13
Waiters attending meetings ...
3 >7
Coals and Gas
16 12
II
Repairs
4 6
Sundries
14 14
2
Mrs. Jackson's annuity, i year
8 16
3
193
445 7 6
21 13 1
242 12 6
124 12 3
Balance at Banker's 307 17 2
£1335 2 6
Audited and found correct, this twenty-sixth day of January, eighteen
hundred and sixty-six, by us^ the undersigned duly appointed Auditors of the
Society,
John Browning,
S. M. Drach,
^ William Simms.
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g6 Report of the Council
Assets and Present Property of the Society, January i,
1866:-
£ «.
d.
£ *.
d.
Balance at Banker's
...
..
...
307 17
2
I Contribution of 7 yean
' standing
14 14
I „
6
It 12
* *>
5
21
4
4
33 "
4 M
3
25 4
40 M
2
.. 168
40
I
84
2 >«
▼arious sums
10 15
369 17
Due for Publications of the Sodety
..
...
3 4
6
j^i 300 Consols (including the Lee Fund).
j^5ooo New 3 Per Cents (including Mrs. Jackson's Gift).
Unsold Publications of the Society.
Various astronomical instruments, books, prints, &c.
Balance of Tumor Fund (included in Treasurer's Account) 92 1 1 5
To the Council of the Royal Astronomical Society
of London,
Gentlemen, — We, the undersigned, duly appointed Auditors
of the Society's Accounts for the year ending 31st December
last, have this day searchingly investigated the same, and find a
cash balance at the Banker's in favour of the Society of three
hundred and seven pounds seventeen shillings and twopence
(£307 17*. 26?.), which includes one shilling and one penny
petty cash overpaid by and due to your Assistant Secretary.
We find further that the Funded Stock now possessed by
the Society amounts to five thousand pounds New Three per
Cents, and two thousand three hundred pounds Consols, yield-
ing dividends of £219 per annum.
We further beg to record our unanimous conviction that
the Accounts of the Society, as presented to us, have been
kept with unnecessary complexity ; and we earnestly recom-
mend a return to the simpler method formerly adopted.
As witness our hands, this twenty-sixth day of January,
eighteen hundred and sixty-six.
S. M. Drach,
John Browning,
William Simms.
Ibnyal Astronomical Society* 8 ApartrntntSf
Somerset House, London,
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to the Forty •Hxth Annual General Meeting.
97
The following Revenue Accoant and Balance Sheet, which
are made out in accordance with the plan adopted for the year
1 863, show the exact position of the Society both as regards
assets and liabilities : —
REVENUE ACCOUNT for thb Ybar
To Composition fond
Tumor fond
Lee fond
Mrs. Jackson
Rent
Editor
Printing
Engraving
Biading
Assistant- Secretary
Collection
Law
Taxes
Postage
Parcels
House Expenses
Coals and gas
Meetings
Medal
Insurance
Repairs
Sundries
Sums written off
To Capital — increase
By New compositions
Composition fund — deaths
Admission fees
First year's contributions
Annual contributions
3 Ykar
£ 9.
1865
Dr.
£ 9.
189
d.
15
3 5
8 16
6
3
»7 I
9
60
145 8
8 IS
» 9
6
9
8
100
33
348 13
II
6
21 15
II
34 "5
2
4 19
22 18
I
8
18 8
II
17 10
10 10
10
6
4 6
22 2
2
173 4
5
38 17
SCO 5
II
539 a
II
£
"77 3
Cr,
£ 8.
d.
...
..
189
...
••
105
60 18
...
••
34 13
554 8
Carried forward £943 19 o
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98 Report of the Council
Brought forward JB943 19
Dividends
1, January ^^30 14 3
M
April 68 14 9
»»
July 30 19 6
f*
October 73 15
204 3 6
Sale of publications
74 8
By Inv
esting
under par
BALANCES, December 31, 1865.
54 12 6
€1277 3
Dr.
Cr.
£ 8.
d.
£ ». d.
Cash due to Assistant- Secretary
oil
307 17
2
Banker's balance.
Proceeds of Tumor fund
92 II 5
Proceeds of Lee fond
659
Due to Mrs. Jackson
- - -
369 17
Annual contributions — arrears.
Paid in advance
660
8 8
Admission fees — 4 due
3 4
6
Due for publications.
Reserve against annual contributions due ..
65
2300
3 per Cent Consols at par.
,, Tumor fond
500
„ Lee fund
no
5000
New 3 per Cents at par.
,f Jackson fund
300
Estimated liabilities for work in progress
26 3 6
10 10
Medal in stock.
- -
-
Unsold publications.
*~
Books and instruments.
Composition fond ... ^^3507
Net capital 3386 8 11
6893 8 II
£7999 i<
3 8
^7999 16 8
Before the other business of the Meeting was proceeded
with, a discussion arose respecting the best mode of keeping
the Financial Accounts and of presenting them annually to
the Society, whereupon the following Resolution was duly
proposed, seconded, and carried : —
" That this Society recommends that the Financial State-
ment be left exclusively in the hands of the Treasurer,
who is to draw up the Accounts in conformity with the
Bye-Laws."
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to the Forty-sixth Anntial General Meeting,
Stock of volumes of the Memoirs : —
Vol
Total
Vol.
Total.
Vol.
Total.
I. Parti
i6
XI.
194
XXI.
10 1
I. Part 2
57
XII.
201
(together).
XXII.
192
II. Part I
75
XIII.
215
XXIII.
190
II. Part 2
39
XIV.
402
XXIV.
193
III. Part I
91
XV.
183
XXV.
208
III. Part 2
110
XVI.
207
XXVI.
214
IV. Part I
no
XVII.
185
XXVII.
472
IV. Part 2
122
XVIII.
185
XXVIII.
432
V.
137
XIX.
198
XXIX.
459
VI.
157
XX.
190
XXX.
216
VII.
180
XXI. Parti
316
VIII.
167
(separate).
XXXI.
XXXII.
.98
130
IX.
171
XXI. Part 2
100
X.
183
(separate).
XXXIII.
258
The instruments belonging to the Society are as follows :—
The Harrison clock,
The Owen portable circle,
The Beaufoy circle,
The Beaufoy transit.
The Herschelian 7 -foot telescope.
The Greig universal instrument.
The Smeaton equatoreal,
The Cavendish apparatus,
The 7 -foot Gregorian telescope (late Mr. Shearman's),
The Variation transit (late Mr. Shearman's),
The Universal quadrant hj Abraham Sharp,
The Fuller theodolite,
The Standard scale,
The Beaufoy clock. No. i,
The Beaufoy clock. No. 2,
The Wollaston telescope.
The Lee circle,
The Sharpe reflecting circle.
The Brisbane circle.
The Sheepshanks^ collection of instruments, viz., —
1. 30-inch transit, by Simms, with level and two iron
stands.
2. 6-inch transit theodolite, with circles divided on silver ;
reading microscopes, both for altitude and azimuth ; cross and
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I oo Report of the Council
siding leyels; magnetic needle; plumbline; portable clamping
foot*and tripod stand.
3. 4*^ achromatic telescope, about 5 feet 6 inches focal
length; finder, rack motion; double-image micrometer; object-
glass micrometer ; two other micrometers ; one terrestrial and
ten astronomical eyepieces, applied bj means of two adapters.
4. 3|-inch achromatic telescope, with equatoreal stand;
double-image micrometer; one terrestrial and three astrono-
mical eyepieces.
5. 2|-inch achromatic telescope, with stand ; one terrestrial
and three astronomical eyepieces.
6. zi achromatic telescope, about 30 inches focus ; one ter-
restrial and four astronomical eyepieces.
7. 2-foot navy telescope.
8. 45 -inch transit instrument, with iron stand, and also Y's
for fixing to stone piers ; two axis levels.
9. Repeating theodolite, by Ertel, with folding tripod stand.
10. 8-inch piUar-sextant, divided on platinum, with coun-
terpoise stand and horizon roof.
1 1. Portable zenith instrument, with detached micrometer
and eyepiece.
1 2. 1 8-inch Borda's repeating circle, by Troughton.
1 3. 8-inch vertical repeating circle, with diagonal telescope,
by TVoughton and Simms.
14. A set of surveying instruments, consisting of a 12-inch
theodolite for horizontal angles only, with extra pair of parallel
plates; tripod staff; in which the telescope tube is packed;
repeating table; level collimator, with micrometer eyepiece;
and Troughton's levelling staff.
15. Level collimator, plain diaphragm.
16. lo-inch reflecting circle, by Troughton, with counter-
poise stand; artificial horizon, with metidlic roof; two tripod
stands, one with table for artificial horizon.
1 7. Hassler's reflecting circle, by Troughton, with counter-
poise stand.
1 8. 6-inch reflecting circle, by Troughton, with two coun-
terpoise stands, one with artificial horizon.
19. 5 -inch reflecting circle, by Lenoir.
20. Reflecting circle, by Jecker, of Paris.
21. Box sextant and 3 -inch plane artificial horizon.
22. Prismatic compass.
23. Mountain barometer.
24. Prismatic compass.
25. 5 -inch compass.
26. Dipping needle.
27. Intensity needle.
28. Ditto ditto.
29. Box of magnetic apparatus.
30. Hassler's reflecting oirde, with artificial horizon roof.
31. Box sextant and a|-inch glass plane artificial horizon.
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to the Forty-sixth Annual General Meeting. loi
32. Plane speculum artificial horizon and stand.
33. 2|-incli circular level horizon, by Dollond.
34. Artificial horizon roof and trough.
35. Set of drawing instruments, consisting of 6-inch cir-
cular protractor; common ditto; 2-foot plotting scale; two beam
compasses and small T square.
36. A pentagraph.
37. A noddy.
38. A small GalileaQ telescope, with the object lens of
rock-crystal.
39. Six levels, various.
40. 1 8-inch celestial globe.
41. Varley stand for telescope.
42. Thermometer.
43. Telescope, with the object-glass of rock crystal.
These are now in the apartments of the Society, with the
exception of the following, which are lent, during the plea-
sure of the Council, to the several parties under mentioned,
viz.: —
The Beaufoy transit, to the Observatory, Kingston,
Canada.
The Sheepshanks instrument, No. i, to Mr. Lassell.
~ " No. 2, to Mr. De La Rue.
No. 3, to Rev. F. Hewlett.
No. 4, to Rev. C. Lowndes.
No. 5, to Mr. Birt.
No. 6, to Rev. J. Cape.
No. 9, to Mr. Lockyer.
No. 10, to Admiral Bethune.
No. 41, to Rev. C, Pritchard.
No. 43, to Mr. Huggins.
The 6-inch circular protractor, to Mr. Birt.
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
Ditto
ditto
The Council cannot recollect any former occasion on which
there has been better ground for congratulation to the Royal
Astronomical Society than at the close of the past year.
Looking backwards ten years, they find the number of the
contributing members has increased by nearly thirty per
cent. The attendance at the Evening Meetings has more than
doubled, and the funded property of the Society, during the nine
years* tenure of office by the present Treasurer, has increased
by upwards of £2700 Stock. Applications for the supply of
the Monthly Notices of our proceedings continue to be made
from every quarter of the globe ; and several of the numerous
private Observatories scattered throughout the country are
showing signs of increasing vitality by the production of fresh
and valuable results.
Time, however, as upon all else, so upon us, has left its
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1 02 Report of the Council
inevitable mark ; and a Society which celebrates, as we do to-
day, its forty-sixth anniversary, can scarcely hope to find many
of the cherished names of its original founders still remaining
on its lists. Of those eminent and energetic men who met
together as the germ of the Royal Astronomical Society, on the
1 2th of January, 1820, three only now survive; but it is
worthy of our most grateful observation, that in Mr. Babbage,
Sir John Herschel, and Sir James South (for these are the
three), we recognise names which are among the most honoured
that have adorned our annals.
The Volume of Memoirs will shortly appear. It contains
three Papers, these are, first, a Memoir by Mr. Stone, the First
Assistant in the Royal Observatory, Greenwich ; the title is
'^ On the Accuracy of the Fundamental Right Ascensions of
the Greenwich Seven-year Catalogue for 1 860."
The second Memoir, also by Mr. Stone, is " Constant of
Lunar Parallax."
The third Memoir, " On some peculiar instances of Per-
sonal Equation in Zenith Distance Observations," is by Mr.
Dunkin, also of the Royal Observatory.
To these Memoirs are appended three communications from
Sir Thomas Maclear, entitled —
1 . " Geocentric North Polar Distances of the Moon and
Moon-culminating Stars from Observations made with the
Transit Circle at the Royal Observatory, Cape of Good Hope."
2. " Right Ascensions and North Polar Distances of
Comet I., 1865, derived from Observations made with the 8 J
feet Equatorial."
3 . " Mean Right Ascensions and North Polar Distances of
Comet I., 1 864, derived from Observations made at the Royal
Observatory, Cape of Good Hope, by W. Mann, Esq. First
Assistant,"
The expense of printing these last Papers is defrayed by the
Government.
Obituary.
During the past year the Society has to regret the loss by
death of more than an average number of long-valued and
distinguished Members, some of whom will be greatly missed,
not alone by our own body, but by the wliole commonwealth of
Science. They are as follows : —
Honorary.
The Duke of Northumberland.
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to the Forty-sixth Annual General Meeting, 103
Ordinary Members,
Dr. Burder.
S. H. Christie, Esq.
Benjamin Gompertz, Esq.
J. W. Grant, Esq.
Sir William Rowan Hamilton.
Rev. John Hind.
Sir John Lubbock, Bart.
F. W. Simms, Esq.
Vice- Admiral Smyth.
Associates.
Prof. G. P. Bond, of Cambridge, U.S.
Prof. Encke, of Berlin.
William Corbbtt Bubder was bom at Stroud, Gloucester-
shire, October 30th, 1822. His father was the Rev. John
Border, M.A., who survives him, and his grandfather was
the Rev. George Burder,. the author of Village Sermons.
After serving five years* apprenticeship to an architect in
Bristol, he left that profession, and, removing to London, studied
architectural engraving under Mr. J. H. Le Keux. His
success in this pursuit is shown by the engagement which
Mr. Le Keux afterwards made with him for his services, as
well as by the published portion of an unfinished work entitled
Architectural Antiquities of Bristol^ the illustrations of
which he both drew and engraved.
As a meteorologist he was widely known from his long
connexion with Mr. Glaisher's corps of observers, and by the
notices which he frequently sent to the Times on matters of
meteorological interest. He also published a few years since
a little volume, the Meteorology of Clifton^ containing the
condensed results of ten yes^ra' observations at that place. A
severely accurate and conscientious observer himself, he in-
stinctively detected the want of these qualities in others, and
was always displeased when he found that a scientific state-
ment had been coloured to serve a purpose, or a phenomenon
recorded with a show of precision beyond what the circum-
stances permitted. At the root of this feeling was, doubtless,
the intense love of truth which distinguished him through
life, and was indeed the dominant principle of his character.
To the same cause may be traced the antipathy which he
entertained to the whole race of weather prophets, a class of
persons whom he disliked the more, as they tended to bring
meteorology itself into disrepute among the half-informed.
Li Astronomy, Mr. Burder found a source of genuine
pleasure. A trivial incident shows how early the bent of
his mind in this direction declared itself. A lady who kept a
preparatory school at which he was a pupil when about seven
years of age relates, that on one occasion be insisted that the
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I04 Report of the Council
play-hour^ 1 2 o'clock, had arrived, because he had observed
that at that hour the shadows of the window-bars took a
particular position on the floor, — a very juvenile attempt at a
meridian observation, and it is believed self suggested. He
was ingenious in the construction of instruments, and devised
a portable equatoreal, of which he published an account in
Recreative Science, He abo constructed a clock, the
accurate performance of which surprised and pleased him.
He often employed spare moments in the apparently unprofit-
able task of scouring the heavens with the naked eye for
new comets, and it is remarkable that on two occasions his
search was rewarded. The particulars of these two dis-
coveries (made on March 28, 1854, and June 30, 1861), are
related by the Hon. Mrs. Ward in Recreative Science for
August 1861. His sight was very acute, as was also his ear.
He had a good knowledge of music, and played agreeably on
the flute and violin.
For the last two years of his life increasing weakness con-
fined him almost entirely to his room, and during this period
his mechanical ingenuity showed itself in a great variety of
contrivances adapted to meet his special wants. One of these
was a mirror, so placed as to reflect into his room the image
of a vane erected on the roof of the house. Another was a
ventilating apparatus, constructed so as to convey a constant
supply of fresh external air, brought up to the temperature of
the apartment by passing through a certain length of tube,
and discharged at a point vertically over his face as he lay in
bed. His condition of chest rendering him acutely sensitive
both to cold and impurity of air, he set great value on this
invention, and was led into an extensive correspondence with
persons wliose attention had been attracted by his description
of it in the Timet.
A rather sudden accession of unfavourable symptoms oc-
curred about six weeks before his death, and from this time
no prospect remained beyond a temporary rally. Yet even
through this period he retained an interest in his former pur-
suits, and his love of nature never failed him. One evening
during this time, being told of a beautiful sunset, he requested
a mirror to be placed so as to reflect it, and by this means was
enabled to see it as he lay in bed. His sufferings were at in-
tervals severe, but his mental faculties remained unclouded,
and his last moments were eminently tranquil and happy. He
died on the i6th of October, 1865, at the age of 43, devotedly
beloved by those who stood nearest to Mm, and sincerely
lamented by a wide circle of friends.
Bbnja]|[in Gohpbrtz, a member of the Jewish community,
was descended from a family that long held a distinguished
position in Holland. His grandfather on the mother's side,
Benjamin Cohen by name, was on intimate terms with William
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to the Forttf -sixth Annual General Meeting. 105
Prince of Orange ; and it is related that during the troubled
times of the first French Revolution the Dutch Stadtholder
found a readj asylum at the magnificent mansion erected by
his friend at Amersfort. Benjamin Cohen was a man of
intellectual tastes, evinced, among other ways, by his causing
a translation of Euclid into Hebrew to be made for his use.
The father of Benjamin Grompertz was a successful diamond-
merchant, a pursuit for which the Dutch appear to possess
a singular aptitude even to the present day. The literary
tastes of the grandfather descended to the grandchildren, and
all the brothers of Benjamin Gompertz became, like himself,
men of mark in their generation. His brother Isaac wrote
poems, possessing a merit sufficient to attract the approbation
of Byron. Ephraim Gompertz, still living, is known among a
large circle of acquaintance to be an accomplished and original
mathematician. Lewis Gompertz, the youngest brother, was
the founder of the " Animals* Friend Society," and he enter-
tained and published many a strange speculation on the rela-
tion of the brute creation to man.
Benjamin Gompertz, the subject of this notice, was born
on the 5th of March, 1779, at Bury Street in the City of
London. He did not enjoy the advantage of a collegiate
education, but upon the whole must be considered as a
self-taught man, and to this circumstance, perhaps, may be
attributed some of the originality of pursuit and of concep-
tion for which he was remarkable. He became familiar with
the writings of the French mathematicians of the last century,
but his favourite authors were Emerson and Maclaurin, and
beyond all others Newton. So great an admirer was he of
the latter immortal philosopher, that to the last he retained
his predilection for the *' Fluxional Calculus," not only with
respect to the spirit of its conception, but even for the symbols
of its notation. The form of his mind seems to have been
eminently truthful, and hence, one among other reasons
which he assigned for his rejection of the differential
notation of Leibnitz was, that it was " furtive." ♦ In this
paper, Mr. Gompertz also proposes what he considered to be
certain improvements in the notation of partial fluxions or
differential coefficients, and in the symbols for denoting loga-
rithms and antilc^arithms ; but especially one for the embodi-
ment of zeros which may fairly be considered as a great boon.
Thus, according to Mr. Gompertz, 898,000,000 or 000,000,898
may be written with great convenience 8980 and 0898
respectively.
Mr. Grompertz while still a youth, in fact as early as the
year 1798, took a prominent part among the English mathe-
maticians of the day. He was a constant contributor to the
* " I call the differential notation furtive," says he in the Phil. Tram,
for 1862, ^'on, I think, a moral ground. The moral ground is, that it
appears to give to Leibnitz -a greater claim to originality, to the prejudice of
Newton, than I think he is justly entitled to."
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io6 Report of the Council
ingenious questions contained in the Gentleman's Mathematical
Companion; and the extent of his analytical powers was
fully proved by the fact, that although such men as Ivory,
Nicholson, Griffith, Davies, and others, were constant contri-
butors, nevertheless, from the year 1812 to 1822, and without
a single exception, Benjamin Gompertz carried off the prize
annually offered for the best solution of the prize question.
Young Gompertz was originally intended by his father to
follow a purely mercantile profession, and with this view he
made his first start in life on the Stock Exchange, and con-
tinued a member of that body almost to the time that he
undertook the management of an Insurance Office.
In 1 8 10 he married Miss Abigail Montefiore, the sister of
the well-known philanthropist, Sir Moses Montefiore. Two
daughters still survive this union. The din of Change Alley
was but little congenial to the mind of Benjamin Gompertz,
and, like his eminent friend Francis Baily, he was only too
glad when the hour came that he could retire to the quiet of
his own study, or to the instructive discussions of the various
learned societies of which he became himself an active mem-
ber. It was here that he rejoiced to cultivate a friendly
interchange of thought with such men as Sir John Herschel,
Sir James South, Mr. Babbage, Mr. De Morgan, and many
other well-known names in the household of science.
The first learned society that Mr. Gompertz joined was
the *' Mathematical," whose members met at Crispin Street,
Spitalfields. The object of this society, founded so far back
as 1 7 1 7, was to assist the middle classes in their cultivation
of mathematical pursuits, by affording access to books on
scientific subjects which at that day were accessible to the
opulent alone. In the operations of this valuable society,
Mr. Gompertz took a prominent part, and his great abilities
and constant urbanity there, gained for him so much good
will, that eventually he became President of the society, which
office he retained until the members amalgamated themselves
with the Royal Astronomical Society, and transferred to us
their valuable collection of books and instruments.
In 1 806 Mr. Gompertz contributed his first original paper
of importance to the Royal Society, through Dr. Maskelyne,
the Astronomer Royal of that day. This memoir treats of
the summation of certain series by the method of differences,
which theretofore had been summed by Landen through the
aid of imaginary quantities. It was possibly the composition
of this memoir which induced Mr. Gompertz to direct his
attention to the interpretation and calculus of imaginary sym-
bols, which soon occupied his thoughts for a considerable
period. The results of these speculations he published in a
series of tracts at his own expense, and next to his mathe-
matical expression for the law of mortality, he even considered
them as the most successful of his essays.
In 1819 Mr. Gompertz was elected a Fellow of the Roy3.1
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to the Forty-sixth Annual General Meeting. 107
Society, and for forty-six years he continued an active member
of that illustrious body, and occasionally served as a member of
its Council.
In the year 1820 occurs the foundation of our own Society,
and if Mr. Gompertz cannot be with strictness considered as
one of its actual founders, it is certain that he became one of
its warmest and most active supporters from the day of its
foundation. On Feb. 9, 1821, he was elected on the Council,
and of it he continued a most valuable member for nearly ten
years. Many of the most valuable contributions to the Me-
moirs of our Society were committed to his care, and not a
few thus entrusted to him were elucidated and rendered more
complete by his explanatory notes. Instances of this will be
found in Littrow's paper " On the Transit Instruments,"
(Astron, Trans, vol. i. p. 275), and in KreiPs paper " On the
Equatorial," vol. iv. p. 501.
The first contribution made by Mr. Gompertz to our Me-
moirs was in 1822, on the subject of "The Aberration of
Light ;" and in this memoir occurs a passage which it may not
be inopportune here to transcribe, not alone for the truth
which it contains, but for the sake of the picture which it
presents to us of the enthusiasm with which Gompertz was
animated in his pursuit of science. " In the contemplation of
the sciences," he says, " there is, besides the pleasure arising
from the acquirement of knowledge of practical utility, a pe-
culiar charm bestowed by the reasoning faculty itself in a well-
directed pursuit of facts; and though the results deduced by the
arguments are frequently considered to be the only objects of
value by the unlearned, the man of absolute scientific ardour
will often, while he is enraptured with the argument, have not
the slightest interest for the object for which his argument was
instituted." This remarkable evolution of Mr. Gompertz's
mind may probably serve as the clue explaining the fact that,
although he enriched the Memoirs of the Royal Astro-
nomtcal Society with many admirable contributions on the
subject of the corrections of astronomical instruments, he in no
other sense ever became a practical astronomer, or was much
habituated to the use of the instruments, with the construction
and errors of which he was thus manifestly familiar. Thus
we have in the first volume of our Memoirs (Nov.) papers
and a supplement on the " Theory of Astronomical Instru-
ments." Again, in the volume for 1824, there occurs the
description of a new astronomical instrument, named by
the late Francis Baily " The Differential Sextant." There is
also a contribution on the subject of the corrections due to
errors in the knife-edges of Kater's Convertible Pendulum;
but the most practically important astronomical object to
which Mr. Gompertz directed his attention was that in con-
nexion with formulas for the reduction of the apparent places
of the stars to their mean co-ordinates. What Mr. Gompertz
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io8 Report of the Council
effected in this direction maj probably be most easily under-
stood from the following quotation of words spoken by Sir
John Herschel in his well-known eloge of the late Francis
Baily : '* It seems almost astonishing that these computations,
which lie at the root of all astronomy, and without which no
result can be arrived at, and no practical observer can advance
a single step, should have remained up to so late a period as
the twentieth year of the nineteenth century in the loose and
troublesome state which was actually the case, and that not
from their theory being not understood, but from their practice
not having been systematized. . . . Messrs. Baily and
Gompertz, perceiving this want, proceeded to supply it. The
subject was investigated generally, and a method was devised
for arranging the terms of the corrections for Aberration and
Solar and Lunar Nutations. Some of the tables had abready
been computed, when they heard of Bessel's labours in the same
field. Finding that that astronomer had proceeded on a simi-
lar principle, but that besides the other corrections he had
taken in that of Precession, Messrs. Baily and Gompertz
willingly gave way, and certainly nothing more perfect than
the 'Mementa Astronomica,' by Bessel, could have been
devised. However, Messrs. Baily and Gompertz were of some
use. The complete Catalogue of the Royal Astronomical
Society may be partly looked upon as the fruit of the united
labours of these two men."
Such, then, are the labours of our late most excellent
member in that field of science which we especially cultivate.
With the exception, indeed, of certain investigations, unfortu-
nately left incomplete, on meteors and shooting-stars, which
occupied his attention during a part of the last years of his
life, his most recent contribution to our Memoirs is dated so
far back as the year 1829.
It does not seem to be the province of our Society to re-
cord, more than by way of the most general reference the
labours of Mr. Gompertz in that branch of science in which,
perhaps, no man has ever been more highly distinguished
We allude to his admirable and most valuable contributions to
the theory of Life Assurances and Contingent Reversions,
which never ceased to occupy his thought during the re-
mainder of a long and valuable life. The name of Gompertz
must be fresh in the recollection of every actuary who truly
studies his own profession ; and it may not be too much to say
that his writings will ever form one of the landmarks in a
science which silently but effectually intertwines itself into the
material interests of society.
It is thus that, in a brief paragraph, we simply, as mem-
bers of an astronomical society, pass over a long period of
activity replete with interest to other men whose tastes and
pursuits are attracted or determined by the interest they take
in all that concerns the statistics of human life. In other and
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to the Forty-sixth Anntial General Meeting. 109
more fitting publications they will find the records of these
labours of this remarkable man. To us it must be of interest
to know that, respected by those who saw him only at a dis-
tance, or through the medium of his works, and beloved by his
family and those who saw him in the closer relations of life,
Benjamin Gompertz, at a ripe old age, died on July 15, 1865,
and was buried in the Jewish Cemetery, near Victoria Park.
WiLLiAii Rowan Hamilton, one of the ablest mathemati-
cians that this or any other country has produced, and for nearly
forty years a Fellow of the Royal Astronomical Society, was
bom in Dominick Street, Dublin, in the year 1805. His
father was by profession an attorney, and was long held in
great estimation both for his personal character and his pro-
fessional ability. The branch of the Hamilton family from
which he was descended, originally settled in the north of
Ireland, in the reign of James the First ; and it is said that by
right a baronetcy belonged to the representative of this branch,
a near relative of his own; although the claim could not be fully
supported, owing to merely technical flaws. Thus Hamilton
may have been in some degree indebted for his great and ver-
satile mental capacity to a mixture of race.
William Hamilton is one of those rare instances, where the
promise of early childish precocity has not been disappointed
by the attenuated achievements of riper years. At various
stages of his boyhood, not to say childhood, for the precocity
manifested itself at the early age of four, he is said to have
successively acquired some notable acquaintance with no less
than thirteen languages, European and Asiatic. His attention
was directed to the latter, because it was originally hoped that,
enjoying as he did the opportunity of good patronage, his
career would be passed in India. It is recorded on evidence
which deserves respect, that at the age of seven he was ex-
amined in Hebrew by a fellow of Trinity College, Dublin, and
that '' the child passed a better examination in that language
than many candidates for the fellowship." For obvious reasons
we hope there is some pardonable though very natural exag •
geration in the statement. It is certain however that the
attention of the Persian Ambassador, when on a visit to
Dublin, was attracted by a letter of greeting written in Per-
sian by young Hamilton at the age of fourteen. Whether
or' not any allowance is to be made for the shadow of the
future overlapping the memory of the past, it is quite certain
that the vast intellectual capacities of the boy were evinced
and cultivated at a very early age, and what is of far greater
consequence, this early mental activity did not prostrate or
forestal the successful exertions of maturer life. It is quite
possible that the literary turn thus given to his earlier pur-
suits may have happily laid the foundation of that peculiar
combination of metaphysics and poetry, which distinguished
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some of his mathematical performances from those of most
other men. For his early training in ancient and modern
languages, he was indebted to the loyal care of his uncle, the
Rev. James Hamilton, curate of Trim; but in science and
mathematics he appears to have been nearly self-taught and
self-directed ; in his case, as in that of many other eminent
men, this circumstance probably conduced to the originality of
his maturer conceptions, and to the peculiar style in which he
embodied them.
By the age of fifteen, younsr Hamilton had mastered the
usual course of elementary mathematics, pure and applied ;
and in some instances had become familiar with works of
original research. He appears to have evinced a peculiar
taste for long and difficult arithmetical approximations, and to
have shown himself no mean antagonist in the solution of
numerical puzzles when matched against a certain arithmetical
prodigy, who, coming from America, happened at that time to
be exhibited in Dublin. By the age of seventeen, he had
mastered Newton's Principia, and a year later found him in
possession of most of the processes in the Micanique CHeste,
Meanwhile, and notwithstanding this very unusual advance-
ment in mathematical knowledge, the main culture of his mind
had been classical; and that, not alone from natural predilection,
but on account of the requirements of the collegiate course on
which it was his intention to embark and to compete.
It is almost needless to say that young Hamilton, with a
mind thus disciplined and furnished, entered upon his course
at Trinity College, Dublin, if not without able competitors, at
all events without an equal, whether in literature or mathe-
matics. As might be expected, he carried all before him ;
and when we speak of success in his literary efforts, it must be
understood that we include Poetry in the list, inasmuch as on
two successive occasi<ms he gained the Vice-chancellor's Prize
for English verse. It is to this early and successful cultiva-
tion of the lighter elegancies of scholarship that his friends
were indebted for a vein of poetical thought and expression
which graced alike his correspondence and his conversation,
and which is sometimes observable even in his graver composi-
tions.
It appears that in the year 1822, one year before his en- ^
trance at the University, young Hamilton, now in his eight-
eenth year, attracted the notice of the celebrated Dr. Brinkley
by certain objections which he made to a demonstration pro- ,
pounded by Laplace in the Mecanique Celeste, On being
invited to pay a visit to that well-known astronomer, the young
student thought that he should most properly express his feelings
of respect by carrying in his hands another instance of inde-
pendent research on the osculation of certain curves of
double curvature. This introduction of Hamilton to the
veteran professor laid the foundation of a mutual friendship
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and respect which continued to increase during Dr. Brinkley's
tenure of office.
In the first year of his student life at Dublin, Hamilton,
notwithstanding his close attention to the elementary line of
study necessarily prescribed to under-graduates, nevertheless
engaged himself in a line of original research. .Even before
his entrance at the University he had directed his thoughts to
the difficult subject of Caustics, and having now completed the
memoir, it was read before tlie Royal Irish Academy in 1824.
This paper was referred as usual to the consideration of a
committee of scientific men, who, being struck with the origi-
nality of the conception, and the evidences of analytical power
which it contained, recommended the author to give those
further developments of the subject which evidently lay within
his grasp. The result of this encouragement to the young phi-
losopher was the speedy completion of a memoir which may be
said to contain the germ of a large portion of the noble work
which it was his lot to contribute towards the advancement of
physical knowledge. Instead of an essay on Caustics, his paper
was now enlarged into a wider and more general investigation,
under the title of a " Theory of Systems of Rays." It may
be no exaggeration to say of this memoir, in conjunction with
its subsequent supplements, that it is one of the ablest con-
tributions ever made to our knowledge of the geometry of
optics. Chasles, one of the most distinguished of modern
geometers, speaks of it as " dominant toute cette vaste theorie,^'
Starting from the simple fundamental principle that light,
whatever may be its cause or its constitution, is amenable to
what mathematicians call ** The Principle of Least Action," or,
in other words, probably as true, and certainly more ex-
pressive, amenable to the principle of no waste in nature,
Hamilton, in a train of analytical logic unimpeachable, and
with a mastery over the management of algebraic symbols
probably never surpassed, shows that the theory of a system
of rays reflected or redacted any number of times at given
surfaces, depends on the determination of a single principal
function V, which contains in itself all the properties of the
system of rays, in a manner analogous to that in which the
properties of a curve are contained in its equation. The same
theory is, in the supplements, extended to the more complicated
and recondite question of double refraction in biaxal crystals,
and at length lands the reader in one of the most remarkable
scientific predictions contained in the records of physical itquiry.
But of this prediction we must speak presently.
When the first part of this " Theory of Systems of Rays "
was presented in April 1827 to the Royal Irish Academy, it
will be remembered that Hamilton was as yet an undergraduate
of twenty-one years of age. In this year the Professorship of
Astronomy in Trinity College, Dublin, became vacant by the
promotion of Dr. Brinkley to the bishopric of Cloyne. Such
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1 1 2 Report of the Council
was hia deserved reputation, that, notwithstanding the appear-
ance of other and most formidable candidates in the field, and
although, moreover, he had as yet taken no academical degree,
Hamilton was elected to the vacant chair.
This circumstance is of itself sufficiently remarkable, and
reflects equal honour upon the authorities who ventured to
make the appointment, and on the young geometer who, by
dint of genius and laborious study, was qualified to discharge
the duties of the post. In connexion with this arrangement
there is a point of osculation with our own Society of suflicient
interest to demand our notice. The present Astronomer Royal,
at that time Lucasian Professor of Mathematics in the Univer-
sity of Cambridge, was one of the candidates for the vacant
post at Dublin ; and he too, like Hamilton, had been advanced
to his professorship before he had ceased nominally to be in
pupilage. We are not here, even by the remotest implication,
suggesting a comparison between these eminent men ; such
a comparison would not only be utterly unfitting, but, owing
to the divergence of the lines of research adopted by the
two Geometers, would be wholly impossible. Nevertheless the
thought unavoidably presents itself, that for both parties, and
for the general interests of science, the decision of the Dublin
electors was a happy one. Had it been otherwise, the one, in
all probability, from certain natural tendencies of his mind,
would have become a clergyman — no doubt a most eminent
one — in the Irish Church; while Greenwich and our own
Society might have lost the other.
** There is a Divinity which shapes our ends,
Rough-hew them how we will.**
In 1828 Hamilton became a Fellow of the Royal Astro-
nomical Society, and thus at the time of his decease was among
the oldest, as his name was certainly among the most honoured,
of our members. In 1833 he made known, in one of several
supplements to the " Theory of Systems of Rays," his great
discovery of Conical Refraction. In this memoir, starting
again from the principle of least action, and, as before, con-
ducting the investigation by means of a single Principal Func-
tion, he establishes the entire theory of double refraction; and,
applying it to the case of biaxal crystals, by a new and
simpler method* than that originally pursued by Fresnel,
he obtains the equation to the form of the wave assumed
by the vibrating ether within the crystal. On examining
the form of the wave surface, Hamilton, with remarkable
sagacity, observed that if the theory and the results were
true, a single ray of light incident at a certain angle on a
biaxal crystal, must of necessity pass into it, not as one ray,
* It is but a point of justice to state that Mr. Archibald Smith has
subsequently much improved the simplicity of the process by a very elegant
method of elimination.
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nor even as two rajs, but as a conical sheet of light, and
then finallj emerge as a luminous cylindrical surface. And,
again, his profound and complicated analysis indicated that
there was also a direction within the crystal, such, that if an
internal ray of light passed along it, it would emerge from the
crystal, not as one ray, but as a luminous conical shell. Such
results as these were not only apparently contrary to all
analogy and expectation, but formed, if the experiment could
indeed be made, a species of experimentum cruets of the truth
of the undulatory theory of light. Notwithstanding the diffi-
culty of the case, the experiment was at length successfully
performed by Dr. Humphrey Lloyd, of Dublin, whose patient
ingenuity, and faith in the profound work of the geometer, were
rewarded by the sight, for the first time, of what cannot pro-
perly be called less than the astonishing phenomenon of a single
ray spread out, by refraction in a crystal, into an infinite
number of rays, forming the surface of a luminous cone.
From the sagacity of Hamilton, and of his friend Dr. Lloyd,
thus constraining the little crystal of Arragonite to give up.
Sphinx-like, its secret of ages, our thoughts unavoidably turn to
the parallel case of Adams and Leverrier, who, from a similar
strong faith in the laws of nature and in the logic of geometry,
no* only predicted the existence of a planet heretofore unseen
and unexpected, but indicated the precise region of the heavens,
where, as soon as looked for, it was actually found. We do not
regard such results as valuable only because they corroborate
our conviction of the existence of certain laws whereon we
believe the universe to have been constructed by the Author
of Nature, but still more so because they serve to encourage the
student to persevere in his researches, animated by the fullest
conviction that if truthfully conducted they can only land him
in truth, and leaving the cut bono to be determined by the
appreciations, or the wants, or the curiosities, of men in time to
come.
The Royal Irish Academy took cognisance of Hamilton's
great discovery, and of the profound mathematical skill where-
by it was evolved, by conferring upon him their Cuninghame
medal ; and the Royal Society awarded to him a similar mark
of their appreciation of his merits. In 1837 he was elected
President of the Royal Irish Academy, succeeding * his friend
and early patron. Dr. Brinkley, in the chair, as he had suc-
ceeded him in the Professorship of Astronomy. He retained
this distinguished office for eight years, and on his resignation
he received the thanks of that eminent Academy *' for his high
and impartial bearing in the chair.*'
In 1834 and 1835 ^® communicated to the Royal Society
two papers on " A General Method in Dynamics." Here,
* Dr. Lloyd, sen., was President for two years after the death of the
Bishop of Cloyne. Hamilton succeeded Lloyd.
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1 1 4 Report of the Council
again, he commenced with the same fundamental idea, as that
which he had already so successfully adopted in his " Theory
of Systems of Rays," and he showed that the integration of the
differential equations of motion for any system of bodies may
be considered as depending on the determination of a certain
Principal Function, which he defines in several different forms,
but in each case by means of two partial differential equations
involving, one of them, the differential coefficients in regard
to the final co-ordinates (co-ordinates at the time t\ the other,
those in regard to the initial co-ordinates of the several par-
ticles. He also established in these Memoirs the now well-
known ^^Hamiltonian Form " of the equations of motion of any
material system.
The two Memoirs just referred to gave occasion to Jacobi's
investigations on *^ Partial Differential Equations" (Crelle,
t. xvii. 1837). Jacobi shows that, instead of ^'Hamilton's
Function" involving the time and the initial and final co-or-
dinates, and satisfying two partial differential equations, it is
allowable to consider a function of the time and the final co-or-
dinates only, satisfying a single partial differential equation ;
and he considers that by omitting to make this simplification,
Hamilton presented his remarkable discovery in at least an
imperfect light. There can be no doubt that the simplifica-
tion thus introduced by Jacobi was a most important and valu-
able one ; but it can scarcely be objected to Hamilton that he
failed to perceive all the results deducible from his own dis-
covery, any more than it can be objected to Fresnel that he
left it to Hamilton to deduce conical refraction from the
very form of the wave surface which Fresnel was the first
to investigate. It must not be forgotten that it is to Ha-
milton's discovery as their fountain, though the course of
the stream was directed by Jacobi, that are due all the de-
velopments which have since been made in the vast subject of
Theoretical Dynamics. In a word, it may not be too much
to say that the step in advance made by Hamilton's two
memoirs can only be compared with that effected at an earlier
epoch by the publication of Lagrange's Mecanique Anaiy^
tigue. For this work, also, Hamilton was again awarded a
gold medal by the Royal Society.
We pass over various other characteristic works of this
profound analyst, not because they are devoid of interest or
of worth, but because they are less within tlie scope of our
Society ; and we come at length to what Hamilton con-
sidered the crowning labour of his life, — a labour which for
the next twenty years, and indeed till within a few days of
his decease, continued to occupy his thoughts. The labour
here referred to was bestowed on the invention and the deve-
lopment of the Calculus of Quaternions. In a memoir such
as this, and for the purposes which we have in view, we must
almost despair of explaining, or perhaps of even conveying an
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idea of what is the aim and scope of the Calculus of Quater-
nions, or in fact what a Quaternion is, and yet without some
such attempt, successful or not, any obituary notice of this great
man would be incomplete. For this purpose, then, we must
bear in mind that in the method of geometry intr«Kluced by
Descartes, and which has been retained in astronomical and
physical investigations up to the present time, the position
of a point in space has been determined either by its dis-
tances from three co-ordinate planes, or by what in reality
are their equivalents. Hamilton, however, starts at once by
considering not so much the position of a point, as rather the
relation which exists between two lines intersecting in space,
having regard both to length and to position. It will soon be
seen that in order to determine these relations completely, four
quantities, or four elements, are necessarily involved.
1°. There is the relation which the length of the one line
bears to the length of the other line ;
2°. The angle through which the one line must be con-
ceived to be turned in order that it may coincide with
the direction of the other ;
3°. The plane in which the two lines lie.
And inasmuch as the determination of this plane involves
two elements, viz., 1^. its inclination to some fixed or known
plane, and 2°. an element which is analogous to the longitude
of a planet's node, it follows that four* elements or symbols are
required to determine the relation which one line in space
bears to another line.f The combination of these four elements,
then, forms the Quaternion of Sir William Hamilton; and as
handled and developed by him, these combinations unquestion-
ably form a calculus of amazing generality, grasp, and power.
As an engine of investigation, in the general problem of
* The above is in fact one of Hamilton's many illustrations of the mean-
ing of a quaternion. Analytically speaking, a quaternion is an expression of
the form ip + » d? + ^' y + * ^r, where «,^*, k are imaginary roots of \/~ i, dif-
fering from the imaginaries of ordinary algebra, in that the order of multi-
plication of these symbols is material, ij here not being =j« but = -ji,
and so for the other symbols.
The geometrical interpretation is this : on taking the usual three rectan-
gular co-ordinate axes of XfPtZ; if ij means rotate the axis of (y) round the
axis of (a?) through 90° of right-handed rotation, then j i must mean rotate
the axis of (ac) round the axis of (y) through 90° of right-handed rotation.
Now the result of the former rotation is a line in the direction of the axis of
+ Z'y the result of the latter rotation is a line In the direction of the axis of
— z: in this sense then ij = — Ji and sc j k ^ - kj^ and ik *^ — ki. The
symbol {w) is the ratio of the lengths of two intersecting lines (or rec/or«) con-
sidered in the quaternion. Such is a first glimpse of this intricate Calculus.
t Elements of QuatemionSy Longmans, 1866, page 1 10. This extraordi-
nary work is the result of the unceasing labours of the two last years of Sir
William Hamilton's life : indeed, it is said to have been fatally injurious to
his health. It was all but finished when the lamented death of the author
arrested its entire completion. The Board of Trinity College, Dublin, have
marked their sense of the value of this book by defraying the expenses of its
publication.
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1 1 6 Report of the Council
combined rotations, the method of Quaternions probably has
no rival in completeness or in facility. They remind one of
the tentacles of some gigantic polype, ramifying out into im-
mensity, and bringing back with them the spoils of space.*
It is as yet premature to anticipate on which of his investi-
gations or discoveries Hamilton's fame will ultimately rest.
There are mathematicians among us who in this respect would
be inclined to name his Calculus of Quaternions ; others would
say that none of his writings can overshadow the importance
of his Dynamical TkeoretM, As yet, however, the former
Calculus can hardly be said to be fully developed, or to have
been extensively applied by other philosophers to new lines of
investigation; nevertheless, it can scarcely be supposed that
the persistent and conscientious labour of such a man for
twenty-two succes&ive years can fail to be full of the seeds
of thought, and one day be found to admit and to invite impor-
tant applications. It must however be conceded that (partly
perhaps on account of its comparative novelty, and partly on
account of the metaphysical atmosphere which surrounds it),
the method is neither easy nor attractive to any but the ablest
and most daring of the analysts among us ; many a man who
has essayed to bend this bow has probably said to himself
what Antinous said to his boon companions: —
•* Thou wast not bom to bend
The impliant bow, or to direct the shaft. '^f
We have just spoken of the metaphysical atmosphere
which seems to pervade Hamilton's Calculus of Quaternions; and
herein there is little to excite our surprise, for it was natural for
a man possessed of a mind so versatile and so profound, to
turn it inwards on itself; hence he delighted in metaphysics.
But it was not alone because the culture and bias of his mind
unavoidably led him in this direction, that many of his mathe-
matical investigations assumed a metaphysical turn, but
because he, in conjunction with other thoughtful philosophers,
believed that no further great advance in mathematical science
was now to be expected, excepting from the metaphysical point
of view. Probably it is either a conscious conviction, or an
intuitive perception of this, which influences the peculiar
phase observable in the mathematical investigations of some
of our greatest analysts of the present day.
Hamilton was not only a great mathematician, but by
nature he was also a poet. He was heard to say, '' I live by
mathematics, but I am a poet." If, by this aphorism, he
meant that, had he so chosen, he would have become more
eminent as a poet than he is as an analyst, bystanders might
hesitate to give their assent. Few men, perhaps, are fully
* With this simile Sir W. Hamiltoa expressed his acquiescence to the
writer of this memoir.
t Cowper's translation of the Odyssey, book zzi.
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conscious of the ruling bias and the strong points of their own
minds. We know one of our greatest living philosophers
who would perhaps say, '^ By filial duty I am an astronomer,
but I was born a chemist." Of another it has been often said,
*' He t^ a mathematician and an observer, but he was born an
engineer." Nevertheless Hamilton was a true poet, and by
no means an indifferent writer of true poetry; and it is
quite certain, that some of our subtlest mathematicians are
poets at heart, knowing it and feeling it. And here it may
be worth a passing remark to mention that Hamilton, in his
great Memoir on A. General Method in Dynamics , speaks of
Lagrange's Mecanique Analytique, as a Poem, One of our
chief living astronomers hereon remarks : " Hamilton was
right, but he might have said a poem of most stately rhythm."
The two works of Lagrange and Hamilton have points in com-
mon.
Hamilton counted among his friends, Coleridge, Southey,
Mrs. Hemans, and Wordsworth. It is said, that when the latter,
through Hamilton's enthusiasm, was enabled to get a glimpse of
the inexpressible fascination which surrounds the daring and
creative spirit of modern geometry, the old man was for the first
time inclined to admit even a mathematician into the charmed
circle of the brotherhood of poets. The anecdote rests upon
unquestionable authority: nevertheless, we are inclined to
think better things of so great and profound a mind as that of
Wordsworth, and we are convinced that he must, by sheer dint
of sympathy with other minds, have had at least a suspicion of
the fact before the great analyst revealed it. In vindication
of the justness of these remarks on the expansiveness of great
intellects, and on the poetic power which almost invariably is,
at the least, latent within them, we cannot refrain from quoting
the following Sonnet, written by a great Astronomer, on the
occasion of a visit to Ely Cathedral, in company with Sir
William Hamilton : —
Sunday, July 29, 1845.
The organ's swell was hashed, — but soft and low
An echo more than music rang, — where he,
The doubly-gifted, poured forth whisp'ringly,
High-wrought and rich, his heart's exuberant flow,
Beneath that vast and vaulted canopy.
Plunging anon into the fathomless sea
Of thought, he dived where rarer treasures grow,
Gems of an unsunned warmth, and deeper glow.
Oh ! bom for either sphere, whose soul can thrill
With all that Poesy has soft or bright,
Or wield the sceptre of the sage at will,
(That mighty mace * which bursts its way to light),
Soar as thou wilt, or plunge, — thy ardent mind
Darts on — ^but cannot leave our love behind.
* The symbolic analysis of which the eminent and excellent individual
(Sir W. R. H.) supposed to be addressed has proved himself a most consum-
mate master.— (JBMays by tsir John HeracheL)
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1 1 8 Report of the Council
This Memoir would be incomplete if we did not add, that
our deceased member, together with the character of a scholar,
a poet, a metaphysician, and a great analyst, combined that of
a kind-hearted, simple-minded Christian gentleman; we say
the latter because Sir William Hamilton was too sincere a
man ever to disguise, though too diffident to obtrude, his pro-
found conviction of the truth of revealed religion. Endued
with such qualities as these, what wonder, if of his friends
he was almost the idol, and of his university the pride ; for he
was gentle, and he was eloquent, and he spoke evil of no
man, he defended the fair fame of the absent, and he held con-
troversy with none.
Such, then, is an imperfect but unexaggerated sketch of
this remarkable man. We will only add, that happily he did
not live to survive himself, but in full possession of his facul-
ties, almost in the very presence of the friends who had long
admired him; and, what was no new thing to him, supported
by the convictions and consolations of his faith, he resigned
himself to his rest, as one who knew that he had done a work
which had been given him to do. [C. P.]*
The late Sir John William Lubbock, Bart., born in
1803, was educated at Eton, and at Trinity College, Cam-
bridge, where he graduated in 1825, being first in the Senior
Optimes.
He was many years Treasurer and Vice-president of the
Royal Society, and Vice-chancellor of the University of London;
was a member of most of the principal scientific societies in
this country, of the American Academy of Arts and Sciences,
and of the Academies oi' Turin and Palermo. He spent much
labour upon the theory of the Moon, referred to in Grant's
History of Astronomy y pp. 120-162. He also did much to
improve the theory of the tides, for which he received one of
the royal medals in 1833. The tides in the Nautical Al-
manac were for some time calculated from his tables {Nautical
Almanac, 1848, part xi.).
In conjunction with Mr. Drinkwater Bethune he wrote an
essay On Probability for the Society for the Diffusion of Useful
Knowledge. This treatise, when reprinted, owing to some
mistake of the binder, was described as " De Morgan on Pro-
babilities." This extraordinary mistake was not discovered by
Sir J. Lubbock until the work had been in circulation for
some years ; and Prof. De Morgan, in a letter to the Times,
stated that " he could not, in fifteen years, though using every
opportunity, succeed in restoring the book to its true au-
thors."
* In the preparation of this elogCf the writer has received much assistance
from Dean Graves, P.R.I.A. ; the Rev. R. P. Graves, of Dublin ; and Pro-
fessors De Morgan and Cay ley.
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There can be no doubt that among all the mathematicians
who have written upon the Lunar Theory, confessedly
among the most difficult and most important questions in Phy-
sical Astronomy, Sir John Lubbock has a claim to a most con-
spicuous place. What he says of himself and of his coadjutors,
in his Memoir published in the. Transactions of the Royal
Astronomical Society ^QT i860, is fully within the limits of
justice and truth: "I am confident that a just posterity will
give to us — that is, to Plana, Pontecoulant, and Lubbock, who
in 1 846 furnished the means of constructing tables of the Moon
without any empirical hypothesis — the credit of first bringing
the Lunar Tables within the limits of error of observation, and
thereby of bringing to perfection the solution of the problem of
finding the longitude at sea by means of lunar observations."
Great, very great as is the merit of Sir John Lubbock in
having thus brought the theory to perfection, it is much to be
regretted that he did not take one step more, and that the com-
paratively easy step, of causing the Tables to be constructed.
Sir John Lubbock was one of the Treasurers of the Great
Exhibition of 1851, and was a member of several commissions,
among which we may particularly mention that for deter-
mining the standards, and also that appointed to investigate
the question of weights and measures. He was for many
years senior partner in his bank; and his last publication of
importance was one on the Clearing of the London Bankers,
to which he appended, as a motto, the well-known passage
commencing,
** Atque equidem» extremo ni jam sub fine laborum
Vela traham, et terris festinem advertere proram/'
He resided principally at his seat in Kent, where he took
the greatest possible interest in the education of the neigh-
bouring poor. He also devoted much time to agricultural
pursuits, and was a successful breeder of stock, his south-
downs and shorthorna having carried off many prizes. He
married Harriett, daughter of Col. Hotham, by whom he
leaves eleven children.
The accompanying list contains the titles of Sir J. W.
Lubbock's principal publications : —
On the Theory of the Moon, and on the Perturbations of
the Planets. Eight parts.
Account of the Traite sur le Flux et Reflux de la Mer,
of Daniel Bernouilli.
An Elementary Treatise on the Computation of Eclipses
and Occultations.
Remarks on the Classification of the Different Branches of
Human Knowledge.
An Elementary Treatise on the Tides.
On the Heat of Vapours, and on Astronomical Refraction.
On Currency.
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1 20 Report of the Council
On the Determination of the Numerical Valnes of the Co-
efficients in any Series consisting of Cosines of Multiples of a
Variable Angle.
On Shooting-stars.
On the Attraction of Ellipsoids.
On Cask Guaging.
Note on the Calculation of the Distance of a Comet from
the Earth.
On the Limits upon the Earth's Surface within which an
Occultation of a Star or Planet by the Moon is Visible.
On the Divergence of the Numerical Co-efficients of cer-
tain Inequalities of Longitude in the Lunar Theory.
On the Census.
On some Elementary Applications of AbeVs Theorem.
On the Double Achromatic Object-glass.
On some Problems in Analytical Geometry.
.On a Property of the Conic Sections.
On a Property of the Conic Sections.
On the Wave Surface in the Theory of Double Refraction.
On the Variation of the Arbitrary Constants in Mechanical
Problems.
On the Arabic Names of the Stars.
On the Stability of the Solar System.
On the Proceedings of the Excise Commissioners, with
documents relating thereto.
Table of the Sines and Tangents (natural) for each degree
of the Quadrant.
Table of the Logarithms of the Sines and Tangents for
each degree of the Quadrant.
On the General Solution of Algebraical Equations.
On the Vapours of Ether, Alcohol, Petroleum, and Oil of
Turpentine.
On the Conditions of the Atmosphere, and on the Calcu-
lation of Heights by the Barometer.
On Astronomical Refractions.
On the Gnomonic Projection of the Sphere.
Also, the Stars, in Six Maps.
In 1 860 a most valuable paper, " On the Lunar Theory,"
in the Memoirs of the Royal Astronomical Society.
Fbederick Walter Simms was bom in London on the
24th December, 1803. Being in early youth of very delicate
constitution, some difficulty was experienced in providing him
with suitable employment, until, through the influence of his
brother the late Mr. William Simms with Colonel Colby, he
was despatched to Ireland as a civil assistant upon the Ord-
nance Survey. Active employment in the pure air of the
mountains soon told favourably upon his health, and he re-
turned to England with a tolerably vigorous frame.
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to the Forty 'Sixth Annual General Meeting. 1 2 1
Shortly after leaving Ireland Mr. F. W. Simms became an
astronomical assistant at the Royal Observatory under Mr.
Pond. In the year 1835 he resigned his situation, and re-
turned to his former occupation as a surveyor and civil engi-
neer. He visited France with Mr. Claridge, and joined with
him in the introduction to this country of asphalte for pave-
ments. In 1836 he engaged with the South-Eastern Railway
Company as a resident engineer, a considerable portion of their
works being under his direction. He constructed both the
Bletchingley and the Saltwood Tunnels.
In 1846 the East India Company, having resolved upon
the construction of railways in their territories, made a pro-
posal to Mr. Simms for him to proceed to India as their
consulting engineer, which, after a short delay, was accepted ;
but his health giving way from exposure to the climate, he
obtained leave of absence for some time, and visited the Mau-
ritius. Upon the reinstatement of his health he returned to
his duty, and, amongst other work, he superintended a com-
plete survey of Calcutta, which was executed principally by
native assistants.
Having completed his engagements with the Company,
Mr. Simms returned to England in the autumn of 1851, with
a very shattered constitution, and although careful medical
attention restored him to tolerable health, he lived in retire-
ment afterwards, occupying himself partly by the education of
his son. His death took place in Torrington Square, on the
27th Feb. 1865.
Mr. F. W. Simms was the author of several useful works in
his profession, the principal being a Treatise upon the Instru-
ments employed in Surveying and Astronomy ; a Treatise
upon Levelling ; Practical Tunnelling, He also edited The
Public Works of Great Britain,
Mr. Simms was a member of the Institute of Civil Engi-
neers, and a Fellow of the Geological Society.
Admiral William Henry Smtth was born at Westminster
January 21st, 1788. He was the only son of Joseph Brewer
Palmer Smyth, Esq., of New Jersey, and Georgina Caroline,
granddaughter of the Rev. M. Pilkington. He was a direct
descendant of the celebrated Captain John Smith, who has
been termed the " Saviour of Virginia." During the American
War of Independence Mr. J. B. P. Smyth warmly espoused the
cause of the mother country; but the success of the revolu-
tionists was fatal to his fortunes, and the only compensation
his family ever received for the loss of large possessions, was
the granting of a small annuity to Mrs. Smyth after the death
of her husband, which followed closely on the termination of
the war. At an unusually early age young Smyth followed
the bent of his ardent predilections for a maritime life by
shipping on board a West India merchantman, which for-
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122 Report of the Council
tunately was commanded by an intelligent Master in the Royal
Navy, who took some pains in teaching his protege the rudi-
ments of seamanship and navigation; and it may safely be
asserted that be bad an apt and ready pupil. He afterwards
served in the East India Company's ship Cornwallis; and this
vessel being purchased by bis Majesty's Government and
commissioned ag a frigate under the command of Captain
(afterwards Admiral) Johnston, his long-cherished wish to
serve in the navy was at length gratified. He continued to
serve under the same excellent officer in that vessel, and sub-
sequently in the Powerful, of 74 guns, until she was paid off in
1809, during which period he saw much active service in the
Eastern Seas, notwithstanding the fact that the ship, during a
large portion of the time, was -so crazy as to be hardly sea-
worthy. Mr. Smyth then joined the Milford, of 74 guns, and
again became engaged in active service on the French coast ;
and his vigilance, activity, and courage won the regard and
approbation of his superior oflicers. The Milford was sent to
Cadiz in the autumn of 1810, and immediately on arrival, Mr.
Smyth was appointed to the command of a large Spanish gun-
boat (the Mors-aut-Gloria), manned by a British crew of
thirty -five men, and mounting a long brass 36- pounder and a
6-inch howitzer In this vessel he took an active part in
nearly every operation of the flotilla, operating on the Spanish
Coast. The Mors-aut-Gloria was one of a numerous fleet of
gun-boats, which, from the dash and energy displayed in
handling them, were called " fire-eaters," and among them the
Mors-aut-Gloria was especially distinguished. On one occa-
sion, we are told, she fired upwards of seventy rounds, and
seemed to attract the particular attention of the French gun-
ners ; probably from her superior size, and the conspicuous
death's-head and cross-bones with which her bows were deco-
rated, so that their ricochet shot were constantly splashing the
spray over her, and cut several of her sweeps; yet, strange to say,
she sustained no damage. Notwithstanding the ceaseless vigi-
lance required from Mr. Smyth during these stirring times, he
managed to find time for reading and self-improvement ; and,
indeed, every moment that he could spare from his professional
duties was devoted to hard study. Thus early he laid the
foundation of his future reputation.
It appears that, on his arrival on the Spanish coast, Mr.
Smyth at once embraced every opportunity that presented to
make himself acquainted with the hydrography of the district,
and the knowledge he thus acquired proved of great service in
the prolonged naval operations of the war. Some excellent
charts which he constructed of La Isla-de-Leon and the
neighbouring coast, showing accurately the strength of the
various French and Spanish batteries, having been submitted
to Lord Melville, combined with his own distinguished services
as an officer, procured him a lieutenant's commission, bearing
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to the Forty-sixth Annual General Meeting, 1 23
date March 15th, 1813, which was accompanied by a note of a
very gratifying character from that nobleman.
Almost immediately after the receipt of his commission, he
was appointed to a command in the Anglo-Sicilian fleet at
Messina under Brigadier Sir Robert Hall ; and here we will
take the liberty of making an extract from Marshall's Naval
Biography: —
" One of the first services in which Lieutenant Smyth ap-
pears to have been employed was a confidential mission to the
Court of Naples, then just wavering in its allegiance to Na-
poleon Buonaparte. Early in 1814 he proceeded to Palermo
in command of the Scylla brig, having Sir Robert Hall's flag
on board ; and while there, was exposed to a serious personal
danger. In the night of the 1 9th of February, being on shore
with the Brigadier, he received a report that the Scylla was in
flames. The wind then blew a furious gale, with heavy tor-
rents of rain, and he had the utmost difficulty in getting a boat
launched from Porta-Felice. On rowing a little way out, he
perceived a large ship in flames and adrift, and that his own
vessel was riding in safety."
In April 1814 the abdication of Napoleon put an end for a
time to the European war, and Lieutenant Smyth immedi-
ately applied himself to a minute survey of the Island of
Sicily, of which he executed numerous plans and charts, which
were highly approved by Admiral Penrose, who had been
appointed to the command of the Mediterranean Station, and
were warmly commended by him to the notice of the Board of
Admiralty. He also, at his own cost and without official in-
structions^ carried on an extensive series of hy drographical ope-
rations connecting Sicily with the adjacent coasts of Italy and
with Barbary. These voluntary labours fortunately were ap-
preciated by the authorities at home, who, on September i8th,
1 81 5, advanced him to the rank of Commander, and directed
his charts to be engraved in the Admiralty office. It was also
arranged that Captain Smyth should publish a full description
of Sicily and the neighbouring islands, the Admiralty agreeing
to purchase 100 copies. This work was published in 1824 in
a quarto volume with numerous illustrations, and iVom the
exhaustive manner in which the subject was treated, and the
vast amount of useful information brought together, it attracted
much attention both at home and abroad.
He next became engaged, in company with Colonel Hanmer
Wari'ington, in the collection of numerous specimens of ancient
architecture from the ruins of Leptis Magna in Barbary, which
had been offered to the British King by the Bashaw of Tripoli.
These were afterwards deposited in the Court-yard of the
'British Museum, but were subsequently removed to Windsor,
and have served as models from which many architectural
decorations have been copied.
From the close of the War to the year 1825 he was almost
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1 24 Report of the Council
uninterruptedly employed in his Suryeys of the Mediterranean ;
a labour, the importance of which has been fully recognised.
It is particularly interesting to Members of the Boyal
Astronomical Society to observe that it was during the Survey
of the Mediterranean that Captain Smyth confirmed that intense
love of Astronomy which he retained through life, and to the
advancement of which he afterwards devoted many of the best
years of his life.
Here is his own account of the method pursued in obtaining
the latitudes of the principal points in the Survey : —
^' Many of the principal latitudes were taken on shore with
the 9-inch quintant and artificial horizon, and with the reflect-
ing circle and sextant ; but some of the first-class were obtained
with a fine 15-inch altitude-and-azimuth circle, by means of
sets, with the face of the instrument alternately turned to the
east and the west."
During the prosecution of this survey he formed an inti-
mate acquaintance with the great Italian astronomer Piazzi,
for whose talents and character he entertained a high admira-
tion.
In the year 1 8 1 5 he married Annarella, the only daughter
of T. Warington, Esq., of Naples, a lady of great ability and
rare accomplishments ; and who through all his scientific la-
bours of every description was his devoted companion and
assistant.
Released at length by the publication of his Mediterra-
nean SeOf he resolved to cultivate the taste for astronomy
which he had imbibed, and which, he tells us, "received
its sharpest spur at the close of 181 3, when I accidentally
assisted Piazzi in reading some of the proof-sheets of the
Palermo Catalogue." His first intention was to form a stan-
dard catalogue of the principal stars in the northern hemi-
sphere, by comparison with the standard Greenwich stars, but
fortunately for astronomy he afterwards abandoned the idea of
" grinding the meridian." Acquiring a powerful refracting
telescope in 1830, he resolved to enter "upon a wider scrutiny
of the general sidereal phenomena." Settling at Bedford he
matured his plans, and erected the Observatory which has since
been so fully described in the publications of the Society, as well
as in the work on astronomy which he afterwards published,
that a detailed account of it is here unnecessary, but at the time
of its erection, and for some years afterwards, it was undoubtedly
the most complete and practically useful private Observatory
in existence, and has been the model from which numerous
other private Observatories have been built.
The principal instrument was an equatori ally-mounted
refractor of 5'9-inches aperture and 104* 5 -inches focus, the
optical portion of which was considered to be the chef d'ceuvre
of Mr. Tulley ; the other instruments were a beautiful 30-inch
circle belonging to the Society, and an excellent transit and
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to the Forty-sixth Annual General Meeting. 125
clock. It is worthy of remark that the Equatoreal was the
first, or at any rate one of the first, in this country to which a
clock-work driver was applied, the apparatus being devised by
the Rev. Richard Sheepshanks, and by him presented to Captain
Smyth. Having completed the erection and furniture of his
" Uranian Temple," as he was wont to term it, he devoted
himself, with an energy which has rarely been excelled, to the
micrometrical measurement of the positions and distances of a
numerous list of double and multiple stars, including most of
an ascertained or suspected binary character, and also to physi-
cal observations of a selected list of clusters and nebulae, from
the catalogues of Messier and the two Herschels. The objects
observed were as follows: —
Nebula ..
. 98
Binary Stars . .
. . 20
Clusters
• 7»
Triple Stars . .
.. '46
Stars and Comites ,
. 161
Quadruple Stars
.. 13
Double Stars
. 419
Multiple Stars
. . 21
The more interesting binary stars were observed in some
instances annually, and others were scrutinised at wider inter-
vals. The whole of this work presents an instance of constant
and sustained labour for a definite and distinct purpose during
twelve years such as has not often been excelled in the annals
of extra-meridional astronomy.
The object f )r which the Bedford Observatory was de-
signed having been completed, it was dismantled in 1839;
the Equatoreal was purchased by Dr. Lee, and re-erected at
Hartwell House in a remarkably well-appointed Observatory
designed by Captain Smyth. In making the transfer to the
Doctor, Captain Smyth stipulated for the occasional use of his
old favourite, which was readily conceded; and during a period
of twenty years he continued to make extensive observations
with it, especially after taking up his residence at St. John's
Lodge, within a short distance of Hartwell.
In 1839 Captain Smyth removed to Cardiff^, in order to
superintend the construction of the immense floating-docks at
that port by the Marquis of Bute, but he employed all his lei-
sure hours in arranging and reducing his Bedford observations
for the press. These were all embodied in the work now so
familiar to the amateur astronomer, which appeared in 1844,
entitled A Cycle of Celestial Objects^ a work justly esteemed as
one of the most captivating and popular treatises on elementary
and especially sidereal astronomy in our language. The second
volume of this work forms the "Bedford Catalogue," of 850
celestial objects arranged in order of right ascension, and
embodying the results of all his micrometrical and other ob-
servations. The descriptions of the various objects are en-
livened with a vast amount of general classic and antiquarian
lore, introduced in a most genial spirit. The astronomical value
c
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126 Report of the Council
of the Catalogue is of course mainly dependent on the accuracy
of the micrometrical measures. This has been severely tested by
many observers of experience ; and it may safely be said that
in this all-important element the Cycle will stand the most
critical tests that can be applied. On the appearance of the
Cycle of Celestial Objects the Society marked their apprecia-
tion of its value by awarding their gold medal to its author.
In presenting the medal Mr. Airy, the President for the year,
used these emphatic words : —
^^ My confidence in the exactness of the observations is
purely personal. Knowing the attention which has been given
to the instrumental adjustments, the intentness of the observer
upon his work, the nerve, which is made steady rather than
disturbed by the anxiety to procure a good observation, and
the general skill in the management of the instruments, I can
truly say that if an accurate observation were required I
should desire that it should be made by Captain Smyth." In
handing over the medal he added, " And I beg leave to convey
with it the expression of my own opinion that never was a
medal more worthily earned." It is twenty years and more
since these words were uttered, but every observer of double
stars, every amateur astronomer, will heartily endorse these
sentiments.
The publication of the Cycle by no means terminated the
astronomical labours of Captain Smyth. For many years,
when leisure permitted, he returned to his telescope with all
his old zeal and accuracy ; and his observations, entirely on
objects in the "Bedford Catalogue," were afterwards partly pub-
lished in a quarto volume, entitled jEdes Hartwelliance, but
afterwards in a more complete form in a work entitled Specu'
lum Hartwellianum^ which appeared in 1 860, gracefully dedi-
cated to those who had in any way assisted him in his re-
searches. This work is a supplement to the " Bedford Cata-
logue," containing the results of observations made at Hartwell
between the years 1839 *"^ *^59> bringing up to the latter
date the history of many of the more remarkable double stars.
Among them y Virginis occupies a conspicuous place. Captain
Smyth fortunately observed the perihelion passage of the com-
parison star in 1836, and with such rapidity was it performed
that, although its period is probably somewhere about 180
years, he has actually measured it through a course of position
angle of 270° ! From Captain Smyth's measures alone (but
we must now term him Admiral, for he was gradually pro-
moted to the highest rank) Mr. Hind computed the elements of
its orbit. The result was in remarkable accordance with the
elements deduced by our ablest astronomers from a considera-
tion of ALL the recorded measures of y Virginis. This must
be accepted as decisive testimony to the accuracy of Admiral
Smyth's measures, as well as to his sustained vigilance and skill
through a period of thirty years.
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to the Forty-sixth Annual General Meeting, 127
The same volume contains a history of all the circum-
stances attendant on the discovery of the planet Neptune, and
from the fact of his heing President of the Society during the
warm and animated discussions which this discovery gave rise
to, he had ample opportunities of hearing and weighing every
point in the controversy. For close logic and terse statement of
fact the article in question can hardly be excelled in the circle
of astronomical literature, and it is impossible to rise from its
perusal without a conviction that it is the production of a fear-
less and able man, anxious only for the truth.
The Admiral's last astronomical work was a little brochure
entitled Sidereal Chromatics, which also may be considered
as supplementary to the Cycle, It contains many curious
facts and interesting speculations on the subject of the colours of
stars, and a first attempt to verify the tints by reference to a
distinct and well-defined chromatic scale.
Such was Admiral Smyth as an observer and astronomical
writer. It is not our purpose to trace his career except as an
astronomer, and, as a member of our Society, further than ib
necessary to a correct appreciation of the Man. He has left
his mark on all he touched. As a geographer, a hydrogra-
pher, a numismatologist, and an antiquarian, he was equally
distinguished by the depth of his inquiry, his untiring in-
dustry, and the sagacity of his deductions. A reference to his
works on the Mediterranean and on Ancient Medals, will at
once satisfy the inquiries on these points.
As a member of the Royal Astronomical Society his mem-
ory will ever be revered. He joined the Society in 1821, very
shortly after its first establishment, and from that time to a very
recent period he served it either in the capacity of Member of
the Council, Foreign Secretary, Vice-President, or President.
How he discharged the various duties which these several posi-
tions placed him in can now be only known fully to some of the
older members of the Society. For many years he attended
constantly both our Council meetings and our ordinary meet-
ings. As President during the exciting period before alluded
to, he displayed to advantage the many admirable qualities
of his mind, and by his obvious fairness and impartiality,
though holding strong opinions himself, he guided the Society
in safety, and left on the minds of those engaged in the dis-
cussions of the period the conviction that every body and every
opinion had had fair play.
He possessed most of the qualities necessary for President
of a body like our Society, ample information on every
subject that arose, a memory rarely at fault, courage of
the highest kind, and that happy blending of firmness and
good-humour which both commands and wins. It may be
said, with perfect truth, that the Society has never numbered
among its members one more anxious for its interests, more
faithful in services, or more jealous of its honour.
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128 Report of the Council
After " the Admiral " (as he has been almost invariably
termed of late years) removed to St. John's Lodge, the dis-
tance from town and a tendency to bronchitis rendered his
attendance at our meetings less constant than heretofore, but
his interest in our welfare was unabated, and his counsel often
sought and followed.
For many years he was a member of the Board of Visitors
of the Royal Observatory, where he was always attentive to
business, and gave his hearty support to every measure which
tended to promote the efficiency and usefulness of that es-
tablishment.
As President of the Astronomical Club, he was always
genial and courteous, ever keeping things in happy order, and
by his ready wit and flow of humour compelling the mainte-
nance of good fellowship.
During his residence in London, he was a leading member
of various other scientific societies, and in every one he con-
nected himself with he became at once an influential member.
Of these we may enumerate the United Service Institution, of
which he may be said to have been the founder. He was a
fellow of the Royal, the Geographical, and Antiquarian
Societies. Of late years, though with mental vigour unim-
paired, and a capacity for work as strong as ever, he led a life
of comparative retirement, yet preparing a MS. which is now
in type. He felt the necessity of quiet after so prolonged a life
of activity, and this feeling was deepened by the sudden loss
of a beloved and accomplished daughter a few years ago,— a
loss from which it may be doubted if he ever fully recovered.
He still occasionally came to town, but, as he expressed it,
he " felt his days were over " for taking a prominent part in
public affairs. During the last few years of his life he
suffered at times from a painful disorder, but his general
health was good, and his mind as strong as ever. In the
spring of last year it became evident to his family that age
was beginning to tell upon him to some extent, but it was not
until within the last two or three weeks of his life that any
fears of an impending change were entertained. Early in
September he had an attack, from which, however, he seemed
to recover in a great measure, and was able to drive out, and
to move about in the house pretty much as usual. On Friday
the 8th of September, he was able to take a short drive ; in
the evening he was cheerful as usual, and sufficiently well
to be able to adjust a small telescope, and show the planet
Jupiter to his little grandson, Arthur Smyth Flower, with
whom he chatted in his usual playful manner when talking to
children. This was almost the last act of his life. He re-
tired to bed at his usual hour, and was able to undress with-
out much assistance. A few hours afterwards he was seized
with a sudden suffusion of blood on the lungs, and shortly
afterwards, peacefully and without a struggle, his noble and
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to the Forty-sixth Annual General Meeting. 1 29
gentle spirit passed to its eternal rest. It was a death such
as he wished to die. He dreaded a lingering illness with
gradually decaying mental and bodily faculties. Conversing
with the writer of this memoir on this subject some years
ago, he expressed himself with much feeling, and in his own
expressive phraseology added, " I trust when the * Fell Ser-
geant' does come to me he will strike home." His death
occurred early in the morning of September the 9th, 1865,
and a few days afterwards his remains were laid by the side
of his beloved daughter in the little churchyard at Stone,
near Aylesbury. He was in the 78th year of his age.
It may truly be said of him that whatever he did he did
it with his might. When at his work he tolerated no inter-
ruption, but when his day's work was done he was the most
joyous of companions. He had a great fondness for children,
and used to fill his pockets with new half-pennies, to distri-
bute to those he met in his daily walks. To the young astro-
nomer he was ever ready to lend a helping hand, and when
a new observatory was to be built, he was generally con-
sulted.
His letters were very characteristic of the man, — short,
sharp, always to the point, and sailor-like in phrase. His
handwriting was as clear and legible as the best print, every
letter was distinct, and if ever handwriting showed the
character of the writer it was his.
Admiral Smyth has gone from among us, but he has left
behind him a memory which will long be cherished, and an
example which cannot be too closely followed. Every member
of the Society will join with your Council in the expression of
sympathy with his bereaved widow and family, and in their
admiration of one who was both great and good.* [I. F.]
John Francis Encke, bom Sept. 23, 1791, was the
youngest son but one of the deacon of the Jacobi Church in
Hamburg. Four years after his birth his father died, leaving
the care and the education of eight children to his mother, a
lady of much worth, and happily possessed of great mental
energy.
The first tutor of the boy was Mr. Hipp, a gentleman pos-
sessing considerable aptitude for mathematical teaching ; and to
his honour be it spoken, a man who rendered valuable pecu-
niary assistance to the orphan and moneyless family. Hipp
continued this material encouragement to young Encke even
after the time that he entered the College at Hamburg, well
known as the Johanneum. At this College, then under the
directorship of Gurlitt, who enjoyed a high reputation for
classical learning, the boy-student rapidly advanced, and in
* The writer acknowledges his obligations to Sir John Herschel and the
Astronomer Royal.
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130 Report of the Council
addition to considerable ability in Latin composition, his know-
ledge of Greek was sufficient to enable him to translate and
enjoy the Lyrics of Pindar. Notwithstanding, however, this
early classical training, when the time came for his entrance at
the University, Encke resolved henceforth to devote his atten-
tion mainly, if not exclusively, to the study of astronomy.
But here came a very formidable impediment ; there were
ample funds at the disposal of a poor clergyman's son for a
theological career, but none for the prosecution of so unusual a
study. Nevertheless, such was the acknowledged ability, and
so determined was the inclination, of young Encke, that, as is
happily not unusual in such cases, all the difficulties yielded at
length to perseverance, and to his great joy, in Oct. 181 1, he
found himself at Gottingen, and a student under the celebrated
Gauss.
The very newspapers of Hamburg were at that day com-
pulsorily printed in French ; as a condescension, however, or as
an insult to the inhabitants, a German translation was added ; in
a like spirit even the university matricula of the old " Georgia
Augusta" of Gottingen had the image and superscription of
Jerome Buonaparte printed upon it. No wonder then that
neither Gauss nor astronomy could retain the young student
at his books, but, obeying the impulse which animated the
whole heart of Germany, in the spring of 181 3 he took up
arms and marched to Hamburg for the rescue of his country
from the domination of the French. After the re-occupation
of Hamburg by the foreigner, Encke entered the Hanseatic
Legion, then in process of formation in Holstein and Meck-
lenburg, and there he served as a sergeant-major in the horse
artillery until July 1814. In the autumn of this year he
returned to Gottingen and to his astronomical pursuits, and
for nearly twelve months continued a diligent student of sub-
jects far more peaceable, and far more congenial to his turn of
mind. Nevertheless the return of Napoleon from Elba once more
finds him in a soldier's uniform, but now only for a short period,
and, happily, for the last time. Waterloo and its consequences
restored peace to France and to Europe, and young Encke,
who in peace h«d no taste for soldiership and a uniform, re-
turned, for the third time, to Gottingen and to Gauss. It was
thus in the midst of these stirring and troublesome events, that
the spirits of such men as Franz Encke and Wilhelm Struve
were disciplined and matured.
While Encke was serving as a lieutenant of artillery in the
Prussian fortress of Kolberg, he became acquainted with the
celebrated Lindenau, at once astronomer and statesman, and
after the completion of his studies under Gauss, he was ap-
pointed, by the influence of the former, an assistant in the
observatory of Seeberg, not far from Gotha. In 1820 he
became Vice-director, and in 1822 he was appointed Di-
rector, in the place of Lindenau, who returned to his political
career.
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to the Forty-sixth Annual General Meeting. 1 3 1
It was at Seeberg that Encke commenced and completed
his important work on the *' Transits of Venus in 1761 and
1769," published at Gotha in 1822 and 1824. He also ma-
tured his investigation of the Comet of 1680, and of the
remarkable comet of short period which bears his name.
Zach's Correspondence and Lindenau's Zeitsehrift, about this
period, contain many evidences of his talents and his industry.
During his directorship of the Observatory at Seeberg he was
elected an Honorary Associate of the Royal Astronomical
Society, and at the time of his decease was the oldest foreign
member on our list. In 1824 the Council of our Society
awarded to Encke their gold medal for what Mr. Colebrooke,
the President of that day, properly designated as "the
greatest step that had been made in the astronomy of comets
since the verification of Halley's Comet in 1759." Encke had
long been on the track of his comet. In 181 8 he had suc-
ceeded in identifying it with the Comet of Mechain and
Messier in 1786, and again with the comet discovered by Miss
Herschel in 1795, and with the Comet of Pons in 1805. The
result of his investigations was, that this comet, which astro-
nomers have agreed to designate as "Encke's Comet "(although
he himself always modestly calls it the Comet of Pons), would
make its appearance again in 1822, although it would not then
be visible in Europe. Accordingly our Society had the grati-
fication of presenting to Mr. Biimker their medal for its dis-
covery at Paramatta in 1822, on the same day when they
bestowed a similar mark of approbation, as we have already
stated, on Encke himself, for its prediction.
It was in these Memoirs, that Encke signalised himself
by his systematic and most successful application of the prin-
ciple of least squares to a number of astronomical observa-
tions. For the method itself we are mainly indebted to Le-
gendre and to Gauss, but for the first exhibition of its vast
practical value, we are indebted to the example of Encke. His
mind, indeed, seems to have been pre-eminently arithmetical,
delighting in the orderly and systematic development of what
otherwise and to many would seem an inextricable maze of
figures. Those who knew him best consider that he probably
injured the generality of his mathematical analysis by the fas-
tidious care which he bestowed upon its symmetrical arrange-
ment.
In 1825, at the recommendation of Bessel, Encke was ap-
pointed to the Directorship of the Observatory at Berlin ; the
observatory itself was both improperly situated, and inadequately
supplied with instruments, but ultimately, at the suggestion of
Humboldt, a new observatory was erected at the expense of
the Prussian Government, Encke superintending personally
both its construction and its interior arrangements. And here,
for eight or ten years after its completion, he continued with
much assiduity to observe both with the Transit Circle and
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132 Report of the Council
the Equatoreal ; but his natural tastes did not lie in instru-
mental observations, and after the discovery of numerous small
planets by various observers, he devoted himself with much
success to the investigation of planetary disturbances.
The labours of Encke in reference to the Comet which bears
his name have already been referred to. Having carefully
taken into account the perturbing action of the planets on this
comet during several successive periods, he established the
remarkable fact that there is some extraneous cause in opera-
tion which continually diminishes the comet's periodic time.
This is evidently the effect which would be produced if the
comet suffered a resistance from moving in a very rare ethereal
medium, and accordingly this is the explanation proposed by
Encke, and at present generally accepted by astronomers.
Encke has also, as already mentioned, devoted special
attention to the subject of the perturbations of the Minor
Planets.
In the Appendix to the Berliner Jahrbuch for 1837 and
1838, he expounds in detail the method of calculating these
perturbations which had been long used by himself and other
German astronomers, and which was originally given by
Gauss. In this method the perturbations of the six elements
of the orbit are computed for successive equal intervals of time
by means of mechanical quadratures, and from the values of
the elements thus found for any given time, the co-ordinates
of the body at that time are determined.
Now this method, although a very beautiful one in theory,
is attended with the disadvantage of requiring the determina-
tion of double the number of unknown quantities that are
really wanted, and the calculations which must be gone through
consequently become excessively long.
As the number of the known minor planets become larger,
the want of a readier method of computing their perturbations
became more and more pressing.
Encke was thus impelled to devise a mode of applying the
method of integration by quadratures directly to the differen-
tial equations of motion of the disturbed body, and he published
an account of this new method in the Proceedings of the Berlin
Academy for 185 1. In .this Memoir he refers the place of the
body to rectangular co-ordinates, and he determines the per-
turbations of its movements during successive short intervals
of time by a direct computation of the changes produced in the
three co-ordinates by the action of the disturbing planet.
He estimates that the labour of computation is reduced by
the new method to less than one-half of that required by the
method previously employed.
It should be remarked that Prof. G. P. Bond, in a paper
which was communicated to the American Academy of Arts
and Sciences in 1849, had already briefly explained a method
of calculating perturbations exactly similar in principle to that
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to the Forty-sixth Annual General Meeting, 1 3 3
of Prof. Encke, but the latter was totally unaware of the ex-
istence of this paper when he published his own Memoir, which
enters much more fully into the practical details of the method,
and gives greater prominence to the importance of it as applied
to the case of the minor planets.
By astronomers of the present day it is possible that Encke
may be most highly estimated for the vast improvements which
he introduced into the Berlin Ephemeris. The history of astro-
nomical ephemerides is not a little varied and curious ; a con-
cise account of it will be found in the fourth volume of the
Memoirs of the Royal Astronomical Society, on the occasion
of the Council of the Society presenting Encke, through their
President, with a gold medal, for the part which he had taken
in the improvement of the Berlin Ephemeris. Our own Nau-
tical Almanac^ at that day, viz. in 1830, had fallen or had
remained greatly behind the requirements of Astronomers;
but in speaking of the merits of the foreign Ephemeris, the
report of the Council runs as follows : " A gold medal has
been voted to Professor Encke for the superb Ephemeris of
Berlin. It would be superfluous to dwell upon the merits
of this . well-known work, which, far outstripping all rivalry,
must be considered as the only Ephemeris on a level with the
present wants of the sciences." On presenting the medal, Sir
James South, the President, adds, " With the Berlin Ephe-
meris, an observatory scarcely wants a single book ; without
it, every one." It would, however, be disloyal, though in any
other aspect it may be needless, not to add that what has just
been said of the Berlin Ephemeris of 1830, may with equal
truth be predicated of the Nautical Almanacs from 1834 to
the present date; nevertheless the first impulse came from
Encke and Berlin.
Many other labours of Encke may also be found in the
Memoirs and Monthly Reports of the Berlin Academy, in the
Astronomische ^Nachrichten^ and in four volumes of the
Berlin Observations. He is also well known by the publica-
tion of several excellent speeches, and especially for a me-
morable eloge on the celebrated Bessel.
Encke visited England in the autumn of 1 840, in order to
be present at the meeting of the British Association, and for
the purpose of inspecting the English Observatories. His
account of that journey is a testimony of the deep and pleasing
impression which his hearty reception in England left upon
his memory.
In 1859 Encke suffered from an apoplectic fit, and fore-'
seeing the commencement of disease of the brain, he obtained
leave of absence from his observatory in the spring of 1 863. In
the autumn of the same year, finding a recurrence of the same
symptoms, and knowing what they implied, with a brave heart,
the now aged man explained his forebodings to a physician,
and at once placed himself under his care in an institution for
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1 3 4 Report of the Council
diseases of the brain at Kiel. At the commencement of 1 864
he requested permission to be relieved from all astronomical
work, and until the time of his decease, continued to live in a
quiet, happy state of mind, in the midst of his family, at Span-
dau, near Berlin.
Encke, during the forty years of his professorship at
Berlin, impressed the form and bent of his mind upon many
pupils, who have ably contributed their share in the progress
of astronomical knowledge. There is no greater proof of the
real worth of a teacher, than when his pupils speak well and
lovingly of him. They see the man in his weakness and in
his strength. So it fared with Encke. They bear strong and
uniform testimony to his eminent frankness and truthfulness;
his labours, they say, were incessant, his recreations few ; he
was simple in his manners, and in all his habits temperate.
Towards his coadjutors and assistants he showed a severe
judgment, but he set them a severer example. A man such
as this, absorbed in his work, and shutting himself away from
the outer world, was likely to be sometimes abrupt, or laconic,
or even incautious, in his utterances ; these utterances, from
their bluntness or their truthfulness, occasionally gave offence,
and involved Encke in trouble. As age, however, grew upon him
he became more gentle in his manners, and softer in his address;
and in the presence of those whom he knew and trusted, the
old man would sometimes review his own life, and urge his
favourite pupils to draw from his own experience lessons of
moderation and self-restraint, both in passing their judgments
on the labours of others, and in the amount of labour which
they felt it their duty to exact from themselves.
There occurs but one more question regarding this great
and venerable man ; the writer of this memoir gladly adopts
this language, great and venerable^ because they are the very
words selected by men who served him long and who knew him
well, and who are themselves doing good publiR service in their
own day. It is well known that great theological activity, not
to say theological strife, surrounded Encke and every other in-
tellectual thinker in Germany ; it may not, perhaps, concern us,
simply as students in Astronomy, but it cannot fail to interest
us as men, to know what effect this independence of thought and
boldness of expression had upon the spirit of a man, whose
name will for ever be associated with some of the noblest and
furthest-reaching efforts of the human mind. In reply to this
question, we are told by those who knew him intimately, that
Encke retained through life the strength and simplicity of his
early faith ; and we also learn that he was heard repeatedly
to say, that one of the greatest pleasures of his life was de-
rived from the fact, that one of his sons had become a minister
of the Gospel. [C. P.]
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to the Forty-sixth Annual Generel Meeting, 135
PROCBEDINaS OP VARIOUS OBSERVATORIES.
JRoyal Ohservatoryy Greenwich.
The work of the Royal Observatory, Greenwich, during
the past year has been of the usual character. The Moon has
been observed on the meridian, with the transit-circle, and off
the meridian with the altazimuth, at all possible opportunities.
The principal planets have been observed on the meridian with
the greatest regularity. In accordance with a convention
between the Astronomer Royal and the Director of the Im-
perial Observatory, Paris, the asteroids have only been ob-
served at Greenwich during the first half of each lunation.
They have been observed at Paris during the second half of
each lunation.
Considerable progress has been made in obtaining observa-
tions of the stars contained in Bessel's Fundamental which
had not been previously re- observed at Greenwich since Brad-
ley's time.
Many observations of stars have been obtained at the re-
quest of Astronomers who have required places fixed by the
Greenwich Transit for their particular investigations.
The new value of the Mean Horizontal Solar Parallax 8''*94
has been adopted for use in the Observatory. It has also been
adopted for use in the Imperial Observatory, Paris.
The galvanic connexions have remained in perfect order
and without material extensions or changes during the past
year.
The photographic self-registering apparatus for the indi-
cation of Earth currents has been brought into use, and has
furnished some most interesting records during the past year.
The work of the Observatory will be seen to have been
chiefiy directed to the storing up materials for future use in
those branches of Astronomy which fall least readily within
the reach of the Amateur.
Radcliffe Observatory^ Oxford,
In this Observatory no changes of an organic character
have taken place either in the system or subjects of observa-
tion, or the personal staff.
The year, as regards weather fit for observing purposes, has
been below the average, especially during the early and late
portions of it, and this has affected the number of observations,
but not to a very great extent. With the Carrington Transit
Circle, there have been observed 1043 objects, including 113
observations of the Sun, 55 of the Moon, z^oii Mercury, and 18
of Mars. The observations of Venus, Jupiter, and Saturn,
have been given up, as there seems no particular use in mul-
Digiti
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136 Report of the Council
ti plying observations of these bodies, those made at Greenwich
being amply sufficient for all purposes to which they may be
applied. It seems^ however, to be desirable that observations
of the position of the Sun should be generally made for the
purpose of securing an independent determination of the equi-
noctial points of the ecliptic ; and, with regard to the Moon, it
may frequently happen that an observation may be made at an
Observatory on a day when clouds have prevented it at another.
The same remark applies to observations of Mercury^ which
are necessarily scanty, and in which the Hadcliffe Observatory
has been particularly successful.
The heliometer has been used by Mr. Main for observa-
tions of Struve's Lucidce, as in the preceding year; but, nearly
all the stars in Struve's first Appendix, at large distances
from each other, have been added to the list, together with the
stars having conspicuous proper motion included in his second-
Appendix.
Some occultations of stars by the Moon have also been ob-
served with the heliometer telescope, and thoroughly reduced.
The heliometer is now in a very complete state of repair and
adjustment. The error of elevation of the areas which existed
in former years has been accurately corrected, and a much
simpler means of conveying the galvanic current for the illu-
mination of the scale has been adopted. Failures of the light
rarely occur now, and when they do happen, they are generally j
traceable to the battery, to which a very simple and easy test 1
is applied.
The meteorological observations and discussions have been
kept up with the same vigour and success as in former years ;
and in the records of recent gales, which have been unusually
protracted and severe, a good stock of materials exists for
comparison with other Observatories, with a view to the ad-
vancement of the theory of storms.
The reductions of the astronomical observations are in a
very advanced and satisfactory state, Mr. Main having de-
voted a great portion of his own time to them.
The reductions of the astronomical observations of 1864
are completed, as well as the Right Ascensions of 1865, ex- i
cepting in the latter case the completion of the reductions to ^
mean right ascension of the stars not used for clock or azimu-
thal error. The Right Ascensions of 1864 have also been
written out into ledgers, and compared with the B. A. C. and
other Catalogues; and the catalogue of all stars observed in
1 864 (including 1 208 stars) has been formed.
AH the observed Right Ascensions of planets to the end of
1865, have been compared with the Nautical Almanac, and
the mean times have been computed.
The printing of the astronomical portion of the volume of
the Radcliffe Observations for 1863 is very nearly completed;
and Mr. Main was enabled, some time since, to distribute a
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to the Forty-sixth Annual General Meeting, 137
few copies of the Catalogue of 1 1 1 5 stars observed in that
year.
A little has been done additionally towards the completion
of the Catalogue of Stars observed between the years i'854
and 1861, but the necessity of providing for the daily routine
of work, and the reduction of the observations, taxes the
energies of the small personal establishment of the Observatory
to such an extent, as to leave little time for other subjects
which admit of some delay.
Cambridge Observatory,
The objects kept mainly in view in the Cambridge Obser-
vatory for the year 1 865 are —
1. A determination with the meridian instruments of the
stars to which M. Oeltzen has assigned considerable proper mo-
tions, by a comparison of the Histoire Celeste with Argelander's
Northern Zones. The original intention of obtaining ^ye in-
dependent observations of each star with the transit instrument
and mural circle has been adhered to, and a large proportion of
the requisite observations is now completed.
2. The observations of Argelander's list for standard stars,
given in the Ast Nach, No. 1540.
3. The usual observations of the Sun about the times of
the equinoxes and solstices, and of the larger planets at opposi-
tion.
4. The Northumberland Equatoreal has been employed
chiefly in observing Faye's Comet, seeking for Biela's, observ-
ing the occultations of stars by the Moon, and examining
the surface of the Sun. Suitable improved eye-pieces have
been provided and used for these purposes.
5. The reductions of the observations, which had fallen
considerably into arrear
The means of the transit and circle observations are taken,
and the corrections for irregularity of pivots in the former
and for runs in the latter are applied to the latest date of the
observations. All the small corrections for the Transit In-
strument are applied ; the clock errors, obtained to the end
of August 1865, and the true north polar distances to the end
of 1864.
Some changes have been made in the observations, furnish-
ing data for instrumental corrections. The pivots of the Tran-
sit Instrument have been carefully examined through the entire
revolution, at equal intervals and at important points, and some
interesting results are the consequence. The collimation errors
are obtained independently of reversal, very frequently in each
position of the instrument, by the aid of Bohnenberger's eye-
piece, and by direct and reflection observations of slow stars,
chiefly Polaris and ^ Ursce Minoris, In fact, this and all the
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138 Report of the Council
other small corrections are found out, as far as possible, every
night that is favourable. As there are frequent and irregular
changes in the runs of the microscopes of the Mural Circle, it
ha^een the practice for some time to take the runs with each
observation.
Royal Observatory, Edinburgh.
Mr. Fiazzi Smyth states that the only instrumental changes
in the Royal Observatory, Edinburgh, since the last Report,
have been two clock-improvements of local invention. The
first is a dynamical regulation of ingenious construction by
Messrs. Ritchie and Son, to the escapement of the " loud
sidereal seconds- striking clock," for the equalization of its ad-
jacent beats ; which are now brought by this contrivance as
close to perfection in that way, as the transit-observer can
possibly desire. The next is a new, and in practice most
satisfactory, method by Mr. Lang, both for first bringing a
normal mean-time clock to a small rate without stopping it
to make alterations on the pendulum, and then correcting its
indications each day, if required, to any small fraction of
a second without interfering with the goodness of its rate
during the remaining twenty-four hours.
Observations of star-places with transit instrument and
mural circle have been going on as usual ; together with the
furnishing of the public with true time through means of the
three several methods of time-ball, time-gun, and controlled-
clocks.
The reduction of meteorological observations for the Regis-
trar General of Scotland has also been in continual progress, and
occupies a large share of time, the number of observing stations
being fifty-five ; and it is only too apparent that until meteoro-
logical theory is very much improved, the number cannot be
reduced.
Thanks to the excellent performances of their duties by the
two assistant astronomers, the above never-ending tasks were
not sensibly interfered with by the absence of the Astronomer
Royal of Scotland in Egypt during several months of last
winter and spring. This visit had resulted from an inquiry
which circumstances had called on him to take up connected
with the principal observational facts, many of them astro-
nomical, of the Great Pyramid ; an inquiry merely literary at
first, but soon demanding an actual repetition of the chief
observations at the place ; so that it was rather fortunate it
should have fallen on the only Director of an Observatory who
is officially non-resident.
The observations, — which were much facilitated by the
liberal condescensionsofHIsHighnesstheViceroy of Egypt, and
which acknowledged the importance of the three great epochs
of modern investigation there, viz.. Professor Greaves in 1639,
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to the Forty 'Sixth Annual General Meeting, 1 39
the French savans in 1799, and Colonel Howard- Vyse in 1837,
— were mainly directed in three departments of linear, angular,
and thermal measures, with special reference to all ca?«es of
discordance amongst former observers, as well as the recovery,
where possible, of ancient fiducial marks or surfaces ; in con-
nexion with which it may be mentioned, that the astronomical
bearings of the corner sockets cut in the natural rock of the
hill, marking the original size of the finished monument, were
determined on two sides of the Pyramid by means of a power-
ful altitude-azimuth circle reading by microscope micrometers.
This instrument was likewise carried to the top of the Pyramid,
and also into the interior, and wherever there were important
angles requiring accurate measurement.
The investigation lasted through no days of continued work
on the spot, and its records are now in course of preparing
for publication.
Glasgow Observatory.
The operations at the Glasgow Observatory during the past
year have been mainly of the same character as in former
years. The transit circb is still employed in the observation
of stars included chiefly between the sixth and ninth magni-
tudes. A few observations of the minor planets have also
been made with the instrument. The Ochtertyre Equatoreal
has been used to a great extent in micrometric measurements
of double stars, a list of such objects having been selected for
the purpose from Struve's great Catalogue. The chief novelty
of the operations during the past year has been the deter-
mination of the longitude of the# Observatory, by means of
galvanic signals exchanged on several nights with the Royal
Observatory, Greenwich. An account of this operation, the
result of which was very satisfactory, has been recently pub-
lished in the Monthly Notices. The arrangements for the
transmission of true time to the city and port of Glasgow
which have occupied so much of Professor Grant's attention
during the last two years are now established on a permanent
footing. Jones's invention for regulating clocks by electricity
is used on an extensive scale in connexion with the Observa-
tory, and the results afford a complete confirmation of Mr.
Hartnup's previous experience, as regards the admirable pre-
cision and practical utility of the method.
Liverpool Observatory.
At Liverpool, Mr. Hartnup has been engaged during the
past year in making arrangements previous to the removal of
the Observatory from the Waterloo Dock pier-head to Bidston,
about three miles west of its present position. Considerable
delay has been caused by the excavation of stone for the new
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1 40 Report of the Council
building, from the site on which it is now being erected.
Some practical good will result from this having been done,
as the underground accommodation which has been provided
will be of great advantage for all investigations requiring uni-
formity of temperature. The space around the building is well
adapted for placing the various meteorological instruments in
such positions as to insure results uninfluenced by surrounding
objects.
Preparations have been made for determining the dif-
ference of longitude between the old and new stations, and
observations will be commenced as soon as the new transit-
pier is covered in, so as to protect an instrument which will
be temporarily mounted there. The results of thermometrical
observations taken at both stations during the last twelve
months show that the temperature of the air is lower, and the
daily range much larger, at Bids ton, than it is on the Waterloo
Dock pier-head.
The establishment of a depot near the margin of the river
for the reception and safe custody of chronometers, and for
supplying such rates as can be obtained during the uncertain
time that ships remain in port, has not yet been decided on.
The necessity for such a provision would be greatly diminished
if all chronometers were tested periodically, and mariners
supplied with tables of existing errors.
The Greenwich mean time can be obtained with so much
facility from the time-balls and clocks in Liverpool, that there
is no difficulty in finding the rate in the temperature that
prevails at the time ; but without a knowledge of the cor-
rections due to change of temperature, it is impossible, when
the rate is found in a low or a medium temperature, to say
what the alteration will be when the timekeeper is exposed to
the heat of a tropical climate.
Kew Observatory.
Mr. Balfour Stewart, Director of the Kew Observatory,
reports : —
The Kew Photo -Heliograph has been uninterruptedly at
work under the direction of Mr. De La Rue since the last
report, and during the year 1865 as many as 272 pictures of
the Sun have been taken. The numbers of groups observed in
Kew and in Dessau will in future be annually published in the
Monthly Notices of the Royal Astronomical Society in the same
manner as Hofrath Schwabe has done for the past forty years
in the Astronomische Nachrichten with such benefit to science.
The work of measuring and reducing the Sun observations,
as carried on in Kew, has principally two objects in view ;
first, to bring out in a proper way a great number of facts
calculated to throw light on Solar Physics, and, secondly, to
collect as many accurate observations as possible, in order to
Digiti
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to the Forty -sixth Annual General Meeting, 141
improve the assumed elements of rotation of the Sun, a
problem which the recent and beautiful researches of Car-
rington have rendered more important than ever. A first
instalment of results bearing on the former part of the work
has been published very recently under the title " Eesearches
on Solar Physics by Warren De La Rue, Balfour Stewart, and
Benjamin Leewy, Series I." The results of this investigation
appear to confirm the hypothesis of Wilson, in which spots
are regarded as hollows in the luminous surface of the Sun;
and they also appear to render it probable that the various
degrees of luminosity observed on the Sun's disk are all due to
one cause, namely, the presence to a greater or less extent of a
comparatively cold, absorbing atmosphere. The second series,
which is based on measurements of the areas covered by the
nuclear and penumbral parts of all spots, is in active progress.
This part of the work embraces the whole of Mr. Carrington's
and of the Kew pictures, and will not only be the groundwork
of the immediate investigation for which it is intended, but
promises to extend the foundation for those inquiries which
connect magnetical with solar phenomena.
The Kew researches have greatly gained in scope by the
munificent present of all his observations by Hofrkth Schwabe,
who desired to make them available for the Kew observers,
and also by the liberality with which Messrs. Carrington and
Hewlett have lent their excellent records, thereby placing a
most unique collection of material at the disposal of the ob-
servers. The access granted to the authors by the Royal
Astronomical Society to the observations of Pastorff and Shea
will also doubtlessly prove of great advantage.
For the purely astronomical part of the work which the
Kew Observatory has undertaken, a great many pictures have
already been measured and reduced; and since great care is
taken to perfect the method of observation and render the
photographic record as good a basis for calculation as the
most delicate astronomical observation, there is every reason to
hope that this part of our knowledge will also derive benefit
from the labours of the Kew observers.
A new collimator arrangement for testing sextants, de-
vised by Mr. Cooke, is in course of construction under the
superintendence of Mr. Francis Salter, and will shortly be
erected at the Observatory, so that nautical men will then be
able to have their sextants tested in an accurate manner. It is
also the intention of the Kew Committee to offer to travellers
and scientific observers an opportunity to make themselves
acquainted at the Observatory with portable astronomical in-
struments of every kind, with the mode of using them pro-
perly, and the best methods of reducing observations. It is
unnecessary to dwell on the great benefit which it would
confer on astronomical science, if good use could be made of
such an opportunity.
D
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1 42 Report of the Council
The fundamental determinations for the series of pendulum
observations to be made in India in connexion with the great
Trigonometrical Survey, and for which the Kew Observatory
will form the base-station, have been completed, and a report
of the experiments, submitted to the Royal Society by Messrs.
Balfour Stewart and Loewy, has been published. The instru-
ments have arrived in the best state in India, and the com-
munications which these gentlemen have received from Colonel
Walker and Captain Basevi show that the work there has
already begun and is actively carried on.
Mr, De La Rue's Observatory.
At Mr. De La Rue's Observatory at Cranford the ordinary
routine work has been carried on, and photographs of the
Moon in certain phases have been made from time to time, in
order to fill up lacuna existing in the extensive series already
procured. On October 4th photographs were obtained both
before and during the Eclipse of the Moon, which was nearly
in a state of mean libration ; the pictures procured before the
eclipse are now at the disposal of Mr. Birt, for the preparation
of the skeleton chart of the British Association. The pictures
obtained during the eclipse were found to be in stereoscopic \
relation with those of February 1858, so that when they are . ]
combined with each other, stereoscopic pictures of phases of a
lunar eclipse are presented.
A diligent but ineffectual search was made by Mr. De La
Rue and his assistant, Mr. Reynolds^ for Biela's Comet on se-
veral occasions, on some of which the nights were remarkably
fine. The sweeps were so extensive and so carefully gone
over, that if the comet had been visible with a 13 -inch
reflector, it would have been discovered, even if considerable
errors had existed in the ephemerides.
An Observatory has been built in a position 3"'6 to the
north and o*'23 to the west of the old Observatory, in
which has been erected the Equatoreal formerly belonging to ,
the late Mr. Palmer. The object-glass of this telescope, by
Merz, proves to be a very fine one, but the stand is far too
weak, and will have to be replaced by a better mounting.
The entire Observatory, walls and dome, 1 2 feet in diameter,
revolves easily on a rail fixed to the floor : it is octagonal in
form ; two broad ribs extend from one octagonal face to that
opposite to it, and carry the rails on which the curved shutter
travels ; this shutter, 2 feet 6 inches in the clear, is moved by
a drum, and a handle carrying a pinion which gears into the
wheel of the drum.
Some years ago Mr. De La Rue made photographs of the
Sun on a large scale (three feet in diameter) by means of his
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to the Forty-sixth Annual General Meeting, 1 43
reflector and a secondary magnifier ; the working of this appa-
ratus presented some difficulties, and be has now having con-
structed by Messrs. Cooke and Sons, of York, a refractor for
that purpose, 1 3 inches in diameter and i o feet focal length.
This instrument will be specially corrected for the photon-
graphic rays, and will serve for taking lunar photographs in
the principal focus, as well as Sun pictures, after the rays
have passed through the secondary magnifier. It is antici-
pated that the Sun pictures procured with the new instrument
will set at rest many disputed points in Solar Physics.
Lord Wrottesley's Observatory.
At Wrottesley the past year has been mainly devoted to
the reobserving such of the double stars contained in Lord
Wrottesley's Catalogue of 398, as have rapid orbital motion, or
possess other features of interest. The new driving-clock
constructed on the model of that of Mr. Dawes, which has been
applied to the EquatoreaJ, is very successful, and the Equa-
toreal itself has been much improved by the alteration referred
to in our Memoirs, vol. xxix., p. 86. Although Meteorology
does not fall within the province of our Society, it is not
out of place to mention that a most valuable communi-
cation was made by Mr. FoUet Osier to the British Asso-
ciation at their Meeting at Birmingham, describing the results
of a careful comparison and discussion of the Anemometer
records of Wrottesley and Liverpool. Those persons specially
interested in this subject will have an opportunity of reading
the paper, which has been ordered to be printed in extenso in
the Reports of the British Association.
Mr. Fletcher's Observatory at Tarnbank,
This Observatory is probably entitled to rank among the
best and most complete observatories in private hands in ex-
istence. The chief instrument is a very fine 9* 5 -inch refractor
of 1 2-feet focus, mounted on a long polar axis, which is pro-
bably unique, — it is a single block of cast-iron. The mount-
ing is very fully described in the Notices for last June, and
need not be further alluded to, except to record that, in firm-
ness and ease of motion, it is completely successful. It is
covered by an elliptip dome 18 feet diameter. The other
instruments are a 30-inch transit by Simms, and an excellent
clock by Frodsham. We are informed that Mr. Fletcher is
engaged in re-observing the Bedford Catalogue, a work which
will occupy some considerable time ; and when that is done, it
is his intention to bring out a new edition of Admiral Smyth's
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144 Report of the Council
Cycle of Celestial Otjects, for which purpose the Admiral,
some time ago, made over to him his entire interest in that
work.
Mr, HtLggins's Observatory.
Mr. Huggins has continued during the past year the pris-
matic researches, some of the results of which were given in
the last Annual Report.
On January 4, 1865, he observed the disappearance of
i Piscium at its occultation by the Moon. The result was nega-
tive as to any extensive atmosphere surrounding the Moon.
Mr. Huggins has analyzed the light of about 40 NebulsB
and clusters, in addition to those described in the last Eeport.
All these objects give, with his telescope, either a continuous
spectrum or a spectrum consisting of one, two, or three bright
lines. These bright lines occupy the same positions in the spec-
trum as the bright lines of the nebulae which he first examined.
When the light of a Nebula is dispersed by the prism into a
spectrum consisting of light of all refrangibilities, the spectrum
is extremely faint. On this account it has not been possible
to ascertain whether the continuous spectra, which some ne-
bulae give, are crossed with dark lines, as the solar and stellar
spectra are.
The seven nebulae which follow give a spectrum of one, two,
or three bright lines. Some have in addition a faint continu-
ous spectrum. These gaseous bodies are —
No. 4627 19Z H. I.
No. 2lw2
27 H. IV.
No. 4572
16 H. IV.
4*34
52.
4499
38 H. IV.
4403
17 M.
4827
70s H. II.
The following nebulae and clusters have continuous spec-
tra: —
No. 105 18 H. V. No. 4159 1945 h. No. 4485 56 M.
307 151 H. I. 4230 13 M. 4586 2081 A.
575 156 H.I. 4238 12 M. 4625 51 H.I.
1949 81 M. 4244 50 H. IV. 4627 192 H. I.
1950 82 M. 4256 10 M. 4600 15H.V.
3572 51 M. 4315 14 M. 4760 107 H. II.
2841 43H.V. 4357 190 H. II. 4815 53 H.I.
3474 63 M. 4437 II M. 4821 233 H. II.
3636 3 M. 4441 47 H. I. 4879 251 H. II.
4058 215 H.I. 4473 Auw. N.44. 4883 212 H. II.
Mr. Huggins has made an attempt to determine approxi-
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to the Forty-fifth Annual General Meeting. 1 45
matively the intnnsic brightness of three of the gaseous ne-
bulsB. It is probable that these bodies consist of continuous
masses of material. In the telescope thej present surfaces
subtending a considerable angle. As long as a distant object
is of sensible size in the telescope its original brightness re-
mains unaltered. By a suitable method of observation the in-
tensities of these nebulae have been obtained in terms of the
light of a sperm candle burning at the rate of 158 grains per
hour.
The Light of Nebula 462S i H. IV. ^ ^th part of that of the Candle.
if Annular Nebula in Lyra » sibs^h ,, „
„ Dumbbell 'SehviltL —imi^^ n »»
This estimation, in each case, refers to the brightest part
of the nebula. Nebula 4628 gives a spectrum of three lines,
and also a faint continuous spectrum. The nebula in Lyra
and the Dumbbell nebula give one bright line only. These
values are only approximative, and are too small by the un-
known corrections for the possible power of extinction of space,
and for the absorptive power of the Earth's atmosphere. Simi-
lar observations made at intervals of time may show whether
the brightness of these strange bodies is undergoing increase,
diminution, or periodic variation.
On January 9, 1 866, Mr. Huggins observed the spectrum
of Comet I. 1 866. The comet appeared in his telescope as an
oval nebulous mass, surrounding a small and dim nucleus. The
prism showed that the nucleus was self-luminous, that it con-
sisted of matter in the state of ignited gas, and that this matter
is similar in constitution to the gaseous material of some of the
nebulae. The coma shines by light which has emanated from
another source. Since the extremely diffuse matter of the coma
cannot be supposed to contain solid or liquid matter at the high
temperature necessary for incandescence, it seems almost cer-
tain that the coma reflects the Sun's light. On this supposition,
the prism gives no information whether the material of the
coma is solid, liquid, or gaseous. Terrestrial phenomena sug-
gest a condition similar to fog or cloud. If the luminous gas
of the nucleus suffers condensation and subsequent diffusion to
form the tails of comets, it must pass through a condition in
which it neither emits nor in any large degree reflects light.
Dark spaces are frequently seen between the envelopes of
comets.
The observations in full, of which the results are given in
this Report, have been communicated recently in two papers
to the Boyal Society.
Mr. Birt continues his observations on the Moon's surface
at Hartwell and London, as mentioned in the last Report.
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146 Report of the Council
Daring the past year four forms have been issued by the
Lunar Committee of the British Association for the advance-
ment of Science, viz. No. i for the reception of general ob-
servation of the Moon's surface ; No. 2, a Table of areas for
assisting in symbolizing objects ; No. 3, for recording numeri-
cal and other data, appertaining to each object symbolised;
and No. 4, for aiding in the computation of positions of the
second order. These forms are found to be very useful, and
by means of them nearly 800 objects have been symbolized
and entered, and are now in progress of being inserted in an
outline map of 100 inches to the Moon's diameter, on which
the co-ordinates of each point determined by previous seleno-
graphers, especially Lohrmann, and Beer and Madler, are
being set off in parts of the Moon's semi-diameter to the
fourth place of decimals and the excellent photograph taken
by the President, Mr. Warren De la Rue, just after the
lunar eclipse of October 4, 1 865, and near the epoch of mean
libration, is employed in the delineation of the forms of
objects. As every principal object on the photograph will be
transferred by measurement to the Map, it is expected that a
degree of accuracy will be attained far beyond that which
a filling in by eye-sketching can possibly accomplish. The
most accurate determinations of lunar positions are those of
the first order, but as these are comparatively few and the
triangles formed by them large, amateurs might assist greatly
by increasing their number. It is intended to lithograph por-
tions of the Map now constructing and to distribute them to
observers for this and kindred purposes.
Progress op Astronobtt.
It is extremely difficult, if not impossible, to estimate cor-
rectly the amount of actual progress made in a science such as
Astronomy during any single year. Not seldom the real work
lies for the moment either not wholly matured, or by its very
nature is to be stored away as seed for the harvest of future
years. All that can be done in this direction is to give, so far
as may be, a faithful record of what has actually come to the
surface, and has already found a place in the scattered annals
of learned Societies.
Cometic Structure,
Among the most remarkable and, until a year ago, cer-
tainly among the most unexpected accessions to our knowledge,
is that which this year has come to us latest in the order of
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to the Forty 'fifth Annual General Meeting, 147
discovery. We refer to Mr. Huggins' observations on the
spectrum analysis of the light from a comet. The light of the
nucleus of Comet I. 1 866, as examined under his instrument,
gives a spectrum consisting of but one bright line, whereas
the spectrum formed by the light from the coma gives a spec-
trum which is continuous. The inevitable conclusion to be
drawn from these observations is opposite to that which our
prepossessions would have led us to expect, inasmuch as, con-
sistently with the present state of our physical knowledge, we
are forced to conclude that the light of the cometary nucleus
examined by Mr. Huggins must have emanated from a gaseous
source; whereas, guided partly by other physical considerations,
no doubt remains that the coma contains fluid or solid materials.
Thus the suspicion of analogy between cometic and nebular
matter has received this further confirmation. No doubt dif-
ficult observations of this nature require repetition, but the
known caution and experience of the observer invite our con-
fidence.
BielcCs Comet.
It is possible that in some unknown relation to the struc-
ture of these bodies thus revealed, may stand the fact of the
non-apparition of Biela's dichotomized Comet, up to the pre-
sent date, when the two bodies must have passed their peri-
helion. We are indebted to the labours of Mr. Hind and to
the liberality of Mr. Bishop for the regular supply of ephe-
merides of this remarkable system, but hitherto with no
results : had the comets been visible in Europe, apparently they
must have been detected in the careful and extensive sweeps
made with such instruments as the 15 -inch object-glass at
Pulkowa, and the 13 -inch mirror at Mr. De La Rue's Ob-
servatory.
HoeKs Cometic Hypothesis.
Before dismissing the question of Comets, it seems desirable
to call attention to two interesting papers written by Mr.
Hoek, of Utrecht, on the subject of these bodies, and which
have been inserted in our Monthly Notices. Mr. Hoek con-
siders that he has advanced mathematical grounds whereon
to fouhd the probability that every star is associated with a
cometary system of its own ; but that, owing to . the attraction
of planetary or other cosmical matter, these bodies continually
leave their proper primaries and revolve, either permanently
in ellipses, or temporarily in parabolas or hyperbolas, round
other Suns. Should this hypothesis of Mr. Hoek's be found,
on examination, tenable, a new view of these erratic and
intractable bodies will be opened.
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148 Report of the Council
Retardation of the Time of the EartKs Rotation.
A communication has been recently made by M. Delaunay
to the Academy of Sciences at Paris^ on the difficult question
of the acceleration of the Moon's mean motion. M. Delaunay
thinks that he can satisfactorily account for that outstanding
part of the acceleration which at present appears not to be
accounted for by planetary disturbance.
On the hypothesis that the disturbing forces of the Sun and
Moon act on the lagging protuberance of the great tidal wave,
he considers that the amount of this action is quite sufficient to
produce a progressive augmentation in the time of the
Earth's rotation on its axis, sufficient to account for the
outstanding 6" of the Moon's acceleration. Should this hjrpo-
thesis eventually, and on re-examination, prove to be correct,
it will be worthy of remark, that the scrupulously exact me-
thods of astronomical investigation during the last few years,
will have enabled us to estimate with greater accuracy two of
the prime elements of the solar system, viz., the mean distance
of the Sun from the Earth, and the length of the terrestrial
day. Whether this be the case or not (and no opinion is here
hazarded upon the subject), this remarkable conclusion of M.
Delaunay can scarcely fail to give an additional impetus to
the reconsideration of the more difficult and obscurer parts of
the Lunar Theory.*
Variation of the Eccentricity of the EartKs Orbit.
In connexion, again, with the alteration in the eccentricity
of the Earth's orbit, so intimately related to the former question
raised by M. Delaunay, stand some remarkable speculations
very recently raised or renewed by Mr. Croll relative to the
alleged effects of climatal heat or cold produced in the course
of many thousands of years by the variation in the aphelion
and perihelion distances of the Sun from the Earth. Geologists
give us ample evidence of at least one glacial period, and they
are now beginning to observe indications of a succession of these
periods of refrigeration, separated from each other by very
long intervals of time. No doubt during the course of these
immensely separated epochs there have been cycles of change
in the eccentricity of the Earth's orbit, and it will be the pro-
vince of mathematicians and physicists, possessing competent
skill, to determine how far such a cause is sufficient to account
for a succession of Glacial Periods.
* Since the above was in type, it is understood that the Astronomer Royal
has investigated the effects of the Moon's action on the tidal wave, with results
not in accordance with those of M. Delaunay. Adhuc rub Judice lis est.
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to the Forty-sixth Annual General Meeting, 149
Solar Physics.
There has been much activity exhibited daring the past
twelve months in this interesting- and important field of re-
search, and more especially at Kew. The investigations there
made, in addition to other results not yet published, confirm
the hypothesis of the cavernous nature of solar spots, and of a
downward rush of colder matter from above. In addition to
the observations made at the Observatory itself, Messrs. De
La Rue, Stewart, and Loewy, have availed themselves of all
the drawings and the investigations on the subject within their
reach. . Especially they are measuring the areas of the spots
on the solar surface, as depicted in Mr. Carrington's work,
inasmuch as they conceive that the total amount of spot- area
on the Sun at any assigned time, must be at least one important
exponent of solar activity at the moment in question. In
their confirmation of the truth of Wilson's hypothesis of
the cavernous nature of solar spots, and in their own view of
the downward rush, they are strengthened by the investigations
of M. Chacomac, to whose successful labours on Solar Physics,
astronomers are much indebted. The attention of observers
will be amply repaid by a reference to the notices of M. Cha-
cornac's labours published in the Comptes Rendus of the
French Academy, in relation to the reflective power and the
variable luminosity of the different portions of the photosphere
of the Sun, and to the successive envelopes which appear to
surround that body.
The Rev. J. Hewlett, Mr. Lockyer, Professor Phillips of
Oxford, and Canon Selwyn of Cambridge, have also made
many valuable contributions in the same direction.
M. Faye, from the result of his investigations on the proper
motions of Mr. Carrington's spots, comes to the same conclusion
regarding the downward rush ; but he dissents from the
hypothesis of the Kew observers, that the deficient luminosity
of a solar spot is owing to a diminution of temperature ;
on the other hand, it does not seem possible to harmonize
this objection with the present state of our knowledge of ra-
diant heat.
Again, M. Paye, in a Memoir recently communicated to the
French Academy, on applying to the heliographic longitude of
a Sun-spot the correction due to the parallax which would
necessarily arise from its elevation above, or its depression be-
neath the surface of the photosphere, removes certain apparent
anomalies which otherwise exist in the proper motions of the
Sun-spots contained in Mr. Carrington's work. The following
very interesting conclusions are deducible from M. Faye's mathe-
matical investigation : —
I. Sun-spots are depressions beneath the surface of the
Sun's photosphere, varying in depth from about -jiuth to ^^^yth
of the Sun's radius, i.e. from about 40,000 to 20,000 miles.
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150 Report of the Council
2, Many apparent irregularities in the proper motions of
Sun-spots hitherto supposed to be capricious, or attributable to
cyclones or tornados, or to their own mutual actions, are now
probably explicable by the continued variation in the motion
proper to each successive parallel of the photosphere.
3. The astonishing regularity/ in the motions of Sun-spots,
the maintenance of which is thus demonstrated by M. Faye,
appears to that astronomer incompatible with any hypothesis
of mere superficial or local movements in the photosphere^ but
seems to point to some more general action arising from the
internal mass of the Sun.
Professor Spoerer of Arlem in a memoir submitted to the
Academy of Sciences in Berlin, has obtained a formula which
(from four years' observations) expresses the law for the depend-
ence of the period of the Sun's rotation on the latitude
1= i6°-8475-3° 3812 sin (41** 13' + Heliographic latitude.)
where ( is the angle of rotation in a day.
M. Spoerer, though as it seems on insufficient data, calls in
question Mr. Dawes's conclusion relative to the rotation of the
darkest portion of a spot. Some observations of Padre Secchi
appear to confirm the existence of those peculiar appearances
on the general surface of the photosphere which were first
described as willow-leaves by Mr. Nasmyth.
In addition to the establishment of a photoheliograph at
Wilna, there is a prospect of the erection of a third at Quebec.
If this hope is realized, there will then be a station in England,
in Russia, and in America, by means of which, on account of
the difference of longitude, we may hope to have an almost
uninterrupted self-register of solar phenomena.
Telescopic Diameter of the Moon,
Some important calculations have been made from occulta-
tions of Stars by the Moon as observed at Greenwich and
Cambridge, with a view of ascertaining the difference between
the semi -diameters of the bright and the dark Moon. The result
is that the Greenwich instruments give a telescopic semi-diame-
ter too large by about 2". Mr. Airy considers it probable that
the whole of these 2'^ is due to irradiation ; and he remarks
that, even if the whole of it were supposed to be caused by a
lunar atmosphere, its attenuation must be so great that it would
probably be discoverable by no other mode of observation. It
may here be worthy of remark, that accurate measurements of
Mr. De La Rue's photographs of the great Solar Eclipse of
1 860 give precisely the same results ; a circumstance which
leads to the hope that photography may ultimately become a
valuable auxiliary in even micrometrical observations.
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to ike FoTty-sknth Annual General Meeting. 1 5 1
Meteoric Astronomy,
Meteoric Astronomy is gradually being brought within the
domains of known physical law. Regular observations, when-
ever the state of the atmosphere admits, are made at the Royal
Observatory, at all the epochs of meteoric activity which have
as yet been established or suspected. The well-known periodic
star-shower of November was very diligently and successfully
observed at Greenwich under Mr. Glaisher, at Cambridge
under Prof. Adams, and at Hawkhurst by Mr. Alexander Her-
schel. Very complete preparations having been made at these
three places of observation, the results possess unusual interest
and claim our confidence. A more detailed account will be
given in the Monthly Notices of next March.
Balloon Ascents by Night.
Some very remarkable results have been obtained from
meteorological observations made by Mr. Glaisher during his
intrepid ascents in balloons by night, which may have an
important bearing both on the theory of astronomical refraction
and on the theory of heat.
Mr. Glaisher observed that the decrease of temperature
owing to increase of elevation, was variable throughout the
day, but about sunset the temperature remained constant with-
in the limit of an elevation of 2000 feet. This observation
suggested the probability that after sunset the temperature
might even increase with increase of elevation, at all events
within the same limit of height. Hence arose the proposition
for nocturnal ascents. Mr. Glaisher found that with the aid
of a properly constructed Davy lamp he could read the instru-
ments with sufficient facility, and in December last he made
two ascents, and the results have justified the amount of trouble,
and even of danger encountered in the enterprise. In the
first ascent, when the sky was cloudless, the temperature in-
creased with increase of elevation. During the second ascent,
when the sky was overcast, there was a small decrease of
temperature as the height increased.
In ascents by day, Mr. Glaisher found that the difierence
of the readings of two thermometers, the one having a black-
ened bulb exposed to the Sun, and the other shaded from the
Sun, continued to decrease^ as the elevation increased, until at
the height of about five miles, when the readings of the two
thermometers became identical. Mr. Glaisher considers that
the nocturnal observations deserve repetition and extension.
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152 Papers read before the Society.
Variable Stars.
Mr. Chambers has collected from various sources, and has
published in the Monthly Notices, an interesting and valuable
Catalogue of stars up to this date known to be Variable. It is
herein that an ample field is thrown open to those non-profes-
sional astronomers who possess the requisite means at their
private observatories. The alleged variations in the great
nebula in Oriony and especially the anomalies in the visibility
of some of the small stars in the trapezium recently indicated
by Mr. Huggins, will furnish scope for employment of telescopes
of various apertures.
Mr. J. Gurney Barclay has recently printed a volume of
observations made at his Private Observatory, Ley ton, during
the years 1862-64, for which he merits the thanks of all per-
sons interested in astronomy. Probably the observations of
Minor Planets and Comets published in this Catalogue are
unique as proceeding at this day from a private observatory.
Mr. Barclay very handsomely acknowledges the assistance he
had derived from M. Romberg, now attached to the Royal
Observatory, Berlin.
Dr.Briinnow, lately of the Observatory Ann Arbor, U.S.,
has recently been appointed to succeed the late Sir W. Rowan
Hamilton at Dublin, as Astronomer R03 al for Ireland,
Papers read before the Society from February 1 865 to
February 1866.
1865.
Mar. 10. On the Spectrum of the Nebula in Orion, Prof.
Secchi.
Observations of Comet I. 1 864. Mr. Tebbutt.
Opposition of i/ar5, 1864. Mr. Joy n son.
Drawings of Mars^ Opposition, 1864. Mr. G. Wil-
liams.
Account of a Comet seen in Brazil. Prof. Challis.
On the Date of a Communication of a Mode of Ob-
serving Transits without Reference to Hearing or
Touch. The Astronomer Royal.
Occultations Observed by him. Capt. Noble.
Comet Observations at Sydney Observatory. Mr.
Smalley.
April 1 2. On the Planet Mars. Mr. Joynson.
On an Appearance presented by the Spots on Mars.
Mr. Talmage.
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Papers read before the Society. 1 5 3
Extract from Letter announeing Deaths of Professor
Bond and Lieut. Gilliss. Dr. Gould.
On the Star Baily Lalande 145 1 2 and Neb. H.N. 45.
M. Schultz.
On a New Comet discovered in Australia. Mr. Ellery,
Ditto ditto Mr. Abbott.
Extract from Letter of Mr. Todd on the same Comet.
Mr. Carrington.
Observation of ditto Mr. Abbott.
Ditto ditto Mr. Tebbutt.
Note on the Lunar Theory. Mr. Cayley.
On an Aluminium Bronze Transit Listrument. Col.
Strange.
On the Perturbations of the Planet Neptune, Mr.
Wackerbarth.
May 1 2. On the Notches or Bearings for the Pivots of Transits.
Mr. Yeates.
On some peculiar Instances of Personal Equation in
Zenith Observations. Mr. Dunkin.
Catalogue of Variable Stars. Mr. Chambers.
On the Comets, i860, IIL, 1863, L, and 1863, IV.
M. Hoek.
On the Photosphere of the Sun. Mr. Fletcher.
On a Double-Prism Eye-piece. Rev. W. R. Dawes.
On the Phenomena of Solar Spots. M. R. Wolf.
Discovery of a New Planet (Beatrix). M. De 6as-
paris.
Positions of Comet, 1865. Mr. Ellery.
Second Note on the Lunar Theory. Mr. Cayley.
Note on the Nebulous Star 45 Ij, IV. Geminorum,
Mr. Knott.
Constant of Lunar Parallax. Mr. Stone.
June 9. On an Artificial Horizon. Mr. Merrifield.
Observations of Comet, 1865. Mr, Tebbutt.
Observation of Lunar Eclipse of April 1 1, 1 865. Mr.
Freeman.
Note on ^ Herculis. Mr. Eletcher.
Description of an Equatoreal Mounting. Mr. Fletcher.
Description of an Aperture-diminishing Eye-piece
and a Photometer of Neutral Tint Glass. Rev.
W. R. Dawes.
Observations on the Sun's Photosphere. Mr. Lockyer.
On the Double Star ^ Cygni. Mr. Knott.
Nov. I o. Note on an Error of Expression in two Memoirs of
the Astronomer Royal on the Correction of the
Elements of the Moon's Orbit. Mr. Airy.
Radiant Points of Shooting- Stars. Mr. A. Herschel.
Observations of Solar Eclipse, Oct. 19, 1865. Lord
Wrottesley.
Places of Comet I. 1 865. Mr. Ellery.
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154 Papers read before the Society,
Observations of Encke's Comet. Mr. Tebbutt.
On the Comets of 1697 and 1683, i860 III., 1863 L,
and VL- M. Hoek.
On the Great Sun-Spot of October 1865. Rev. F.
Hewlett.
On the Solar Photosphere. Mr. Fletcher.
Observations on Solar Craters of September 28 and
October 8, 1865. Mr. Brodie.
Occultations of Stars by the Moon. Capt. Noble.
On Photographs of Lunar Eclipse of October 1865.
Mr. Brothers.
On Personal Equation in Beading Microscopes. Mr.
Stone.
On the Telescopic Disks of Stars. Mr. Stone.
On the Physical Constitution of the Sun. M. Cha-
cornac.
On Lambert's Theorem. Mr. Sylvester.
Elements of Comet L 1 865. Mr. Tebbutt.
Expressions for Plana's e, y, Mr. Cayley.
Dec. 8. Observations of Comet IIL i860. M. Moesta.
Observations of Encke's Comet. Mr. Smalley.
On Prof. Krueger's Memoir on a star in Perseus, Mr.
Carrington.
Note on J Herculis, Mr. Burr.
On the Solar Photosphere. Commander Ashe;
Geocentric N.P.D. of Moon and Moon-culminating
Stars. Sir T. Maclear.
Mean R.A. and N.P.D. of Stars compared with Comet
L 1864. Sir T. Maclear.
Mean Places of Stars of Comparison, derived from
Observations with the Transit Circle, and Appa-
rent Places for Dates of Comparison with Comet I.
1865. Sir T. Maclear.
Observations of Solar Eclipse October 19, 1865.
1866. Rev. T. Chevallier.
Jan. 12. Proposition for a Telescope on the Andes. Comman-
der Ashe.
On Sun- Spots. Mr. De La Rue and others.
Ephemeris and Elements of. Comet of December 9,
1865. Dr. Donati.
Observations of n Argus. Mr. Tebbutt.
On the Stars within the Trapezium of Orion. Mr.
Huggins.
On the Diminution of Actinic Effect of the Sun near
the Edge. Mr. Huggins.
Occultation of 1 1 5 Tauri. Mr. Talmage.
On a New Mode of Mounting Silvered Glass Specula
and Diagonal Mirrors in Reflecting Telescopes.
Mr. Browning.
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List of I\iblic Institutions, S^e. 155
List of Public Institutions and of Persons who have contributed
to the Society's Library, S^c. since the last Anniversary.
Her Majesty's Government.
The Lords Commissioners of the Admiralty.
Royal Society of London.
Royal Asiatic Society.
Royal Geographical Society.
Royal Institution.
Royal United Service Institution.
Geological Society.
Linnean Society.
Photographic Society.
Society of Arts.
British Meteorological Society.
British Association.
Art-Union of London.
Institute of Actuaries.
British Horological Institute.
Radclifie Trustees.
Lancashire Historic Society.
Literary and Philosophical Society, Liverpool.
Royal Society of Edinburgh.
Royal Irish Academy.
Royal Dublin Society.
Royal Observatory, Munich.
Royal Observatory, Madrid.
Royal Observatory, Brussels.
Royal Observatory, Palermo.
Observatory, Christiania.
Observatory, Coimbra.
Observatory, Harvard CoUege.
: CoUegio Romano.
L' Academic Imperiale des Sciences de Tlnstitut
de France.
Le D6p6t G^n^ral de la Marine.
Le Bureau des Longitudes.
Imperial Society, Cherbourg.
Imperial Academy, Dijon,
Imperial Academy of Sciences, Vienna.
Royal Academy of Sciences, Berlin.
The Society of Physics, Berlin.
Royal Academy of Sciences, Brussels.
Royal Academy of Sciences, Gottingen. »
Royal Academy of Sciences, Munich.
Royal Academy of Sciences, Amsterdam.
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156
List of Public InstUuHonSy S^c.
Royal Society, Naples.
Royal Academy of Sciences, Madrid.
Royal Academy of Sciences, Bologna.
Royal Institute of Lombardy.
Imperial Academy of Sciences, St. Petersburg.
Academy of Sciences, Batavia.
The Society of Sciences, Geneva.
Canadian Institute.
American Government.
American Academy of Arts and Sciences.
American Philosophical Society.
Academy of Natural Sciences, Philadelphia.
Smithsonian Institution.
Franklin Institute.
American Coast Survey.
Melbourne Public Library.
Royal Society, Tasmania.
Royal Society, Victoria.
Editors of Silliman's Journal.
Editor of the Athenaeum.
Editor of the London Review.
Editor of the Reader.
Editor of the Intellectual Observer.
Editor of the Quarterly Journal of Science.
Editor of Cosmos.
Editor of Les Mondes.
Editor of the Moniteur Scientifique.
G. B. Airy, Esq.
W. Andrew, Esq.
M. Astrand.
Dr. Bache.
J. G. Barclay, Esq.
Joseph Beck, Esq.
E. W. Brayley, Esq.
M. C. Bruhns.
J. Buckingham, Esq.
T. S. Birt, Esq.
R. C. Carrington, Esq.
Dr. T. Claussen.
E. H. Coleman^ Esq.
M. Delaunay.
A. De Morgan, Esq.
S. M. Drach, Esq.
Dr. Draper.
M. E. Dubois.
Dr. Francis.
Prof. A. Gautier.
J. Glaisher, Esq.
S. Gorton, Esq.
Prof. Grant.
P. Gray, Esq.
M. Gylden.
M. C. Haase.
W. D. Haggard, Esq.
J. D. Hailes, Esq.
Prof. Hansen.
R. Harrison, Esq.
J. Herapath, Esq. :
Alexander Herschel, Esq.
M. Hoek.
W. G. Hough, Esq.
M. A. Krueger.
M. C. Linsser.
M. Von Liebig.
M. E. Mailly.
Dr. Mann.
M. Moe'^ta.
Dr. C. Nageli.
H. A. Newton, Esq.
Dr. Peters.
Prof. Plantamour.
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The Presidents Address, 157
J. H. Pratt, Esq. M. O. Struve.
R. A. Procter, Esq. Chas. Todd, Esq.
Prof. Qaetelet. J. Todhunter, Esq.
F. RoUeston, Esq. M. Wagner.
Sig. G. Santini. Rev. T. W. Webb.
Sig. Scarpellini. Dr. A. Wilcocks.
M. H. Sebjellerup. M. Winnecke.
G. R. Smalley, Esq. Prof. R. Wolf.
Prof. Spoerer. Dr. J. C. F. ZoUner.
ADDRESS
Delivered by the President^ Warren De La Rue, Esq., on
Presenting the Gold Medal of the Society to Professor
J. C. Adams, Director of the Cambridge Observatory.
It may be truly said of the Theory of Gravitation that,
while, on the one hand, its fundamental laws are easily appre-
hended by the human intellect, on the other the results which
the application of this theory produces are of so intricate a
nature, especially when the mutual action of more than two
bodies is concerned, that it requires the exercise of the highest
faculties of minds specially cultivated, to trace out all the
consequences which arise out of the mutual attractions of the
particles and masses of matter which constitute the Universe.
No application of the laws of gravitation has given more
trouble to mathematicians than the development of the Lunar
Theory ; frequently, indeed, in the history of physical astro-
nomy grave doubts have been entertained respecting the pos-
sibility of accounting, by means of the grand and simple law
discovered by Newton, for the perplexing inequalities to which
the Moon's motion is subject, and which observation has shown
to exist ; and even the results of observations themselves have
been called into question, when the mathematician has failed
to account for the phenomena they disclose.
It is for most valuable contributions to the development
of this Lunar Theory that your Council have awarded our
Medal to Professor Adams. While it is extremely gratifying to
me to be the medium of explaining the grounds on which this
fiward has been made ; at the same time I am deeply conscious
that it would have been far better, in the interest of science, if
the award had been made under the presidency of a physical
astronomer specially qualified by his previous pursuits to do
full justice to the works of the illustrious mathematician whose
merits we desire, this day, to recognise.
The Medal has been awarded to Professor Adams for His
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158 The President's Address
investigatioDS in respect of the Lunar Parallax and the Secular
Acceleration of the Moon*s mean motion.
I propose first to take into consideration the last named of
these works, which was communicated to the Royal Society so
far back as June 1853, and published in the Philosophical
Transactions^ vol. cxliii. part iii. page 397. It is entitled, "On
the Secular Variation of the Moon's Mean Motion." No con-
tribution to astronomical physics has given rise to more dis- •
cussion in modern times than the investigation of this problem
by Professor Adams ; and it will be in the recollection of most
now present that our Monthly Notices from 1858 to 1862 con-
tain much controversial writing in relation to this subject, in
which several of the most renowned physical astronomers of
the day took part. A summary of the history of this famous
problem is given with remarkable clearness by M. Delaunay in
the Additions cL la Connaissance des Temps for 1 864 ;* and
although I shall borrow from that paper in the course of this
discourse, I would recommend the perusal of the original to all
who may be desirous of acquainting themselves fully with the
subject under consideration.
Let me recall to your recollection that in dealing with the
perturbations caused by the Sun in the Moon's motion, we
have to consider only the differences between the action of the
Sun on the Moon and on the Earth. If both bodies were
attracted equally and in parallel directions, then their relative
motions would not be disturbed, and would be in harmony
with the laws of elliptical motion as derived from the force of
gravitation. But the distance of the Sun from the Moon and
Earth, although great, is not so large but that the Moon is, in
the course of her orbital motion round the Earth, sensibly
nearer to the Sun at one time than at another; moreover,
the angles which are formed by the line joining the Sun
and Moon's centres with the line joining the Sun and
Earth's centres, are sensible, though small. It results there-
from that the attractions of the Sun on the Moon and on the
Earth are generally unequal, and act in different directions ;
and thus arises a disturbing action of the Sun, causing some-
times an increase, sometimes a decrease of the Moon's gravita-
tion towards the Earth ; sometimes a retardation and some-
times an acceleration of the areal velocity ; also continual
changes in the excentricity and inclination of the Moon's
orbit, and in the position of its perigee and nodes; indeed,
producing such a perplexity of inequalities that they can only
be traced to their final result by discussing the effects of the
disturbing forces with all the minuteness of which the re-
sources of analysis permit. It is in the investigation of these
various perturbations that the famous problem of three bodies
consists, " the rigorous solution of which," says Laplace,t
* Pages 21 to 72 inclusive.
t Eafpoaition du Systeme du Monde, 5th Edit. vol. ii., p. 65.
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on Presenting the Geld Medal to Prof. Adams. 1 59
" surpasses the resources of analysis ; but which fortunately
admits of being resolved by approximation, in consequence
of certain favourable conditions in the problem, for example,
the proximity of the Moon to the Earth in relation to her dis-
tance from the Sun." He goes on to say that the most careful
consideration is required to disentangle those terms the in-
fluence of which is sensible, and to determine with exactness
those which, although small in themselves, acquire in the suc-
cessive integrations a sensible value. It will be seen herein-
after that mathematicians of the highest order are liable to
overlook some of these terms, and that consequently no physical
astronomer ought to allow himself to be in the least deterred
from re-investigating a problem because it has passed under the
consideration of men whose names are the greatest in science.
In further elucidation of this reflection, I quote the follow-
ing remarks of M. Delaunay,* who says, " When the extreme
complication of the questions comprehended in Celestial Me-
chanics is taken into consideration, it will be understood that
things do not present themselves to all minds with the clear-
ness which obtains in elementary algebra. By reason of this
complication, problems which are intended to be resolved are
not attacked at once in their entirety ; but divers portions of
the solution are successively sought for in such a manner that
the complete solution may be subsequently obtained by uniting
together the several parts thus separately determined. In con-
sequence of this manner of operating, the greater number of
the equations which are taken into consideration are recorded in
an incomplete form; only those terms are retained which are con-
sidered to have some influence on the partial results sought for,
all the other terms being unexpressed; some of these unexpressed
terms may however have a much greater influence on the Jinal
solution of the problem than those terms which are retained.
The talent of the mathematician who undertakes the discussion
of such questions consists precisely in distinguishing, among
the excessively numerous terms of which every equation would
consist if stated at length, those which ought to be retained as
having some influence on the partial results to be obtained. It
will therefore be understood that a discussion may arise on the
influence or non-influence of certain terms on such and such a
part of the general solution, and consequently on the retention
or rejection of those terms in the investigation of a part
of the solution ; all possibility of such a discussion would
disappear if the complete solution of the question could be at
once and fully undertaken, but this in the greater number of
cases must be considered as beyond the power of the human
mind."
I have been induced to quote from Laplace and Delaunay
their opinions in regard to the difficulties of the analysis, be-
* Additions a la Conn, des Temps, 1 864 , pp. 51, 52.
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i6o The Presidents Address
cause I am sure that during the controyer^y on the secular
acceleration of the Moon's mean motion many persons were
perplexed why any difference of opinion should arise respecting
a question which in reality resolved itself into one of pure
mathematics.
To return to the secular acceleration of the Moon's mean
motion : — you will remember that this inequality was discovered
by comparing records of ancient eclipses with observation
long before theory could account for it. Halley was the first
who suspected its existence; he found, on calculating the
Moon's place for the epochs of certain ancient eclipses recorded
by Ptolemy, by means of her mean motion computed from mo-
dern observation, that the result was such as to indicate a posi-
tion in her orbit less advanced than her recorded place, and the
time of an eclipse so calculated was later than that actually
recorded. He inferred therefore that the angular motion of the
Moon must have been accelerated since the earliest astronomical
records. Halley first alluded to this phenomenon in 1693, and
nearly sixty years elapsed before this suspicion of his was
confirmed. Dunthorne in 1749 communicated a paper to the
Royal Society which contained a discussion of all the observa-
tions calculated to throw light upon the subject; Mayer also
arrived at the conclusion that the Moon's motion had continually
been accelerated from the earliest records. Both the^e astrono-
mers found that the same mean motion of the Moon could not
satisfy both modern observations and the records of the eclipses
observed by the Chaldeans and Arabs. They attempted to re-
present these by adding to the mean longitude of the Moon a
quantity proportional to the square of the number of centuries
before or after 1 700. According to Dunthorne this quantity
should be 10" for the first century; Mayer made it 6"*^ in his
first lunar tables,* and subsequently 9" in his later tables. La-
lande also arrived at the same result as Dunthorne, namely,
9"* 886, which he subsequently fixed at 10" from the year 1700.
Bouvard and Burg also, by discussing a great number of
observations in the two preceding centuries, determined the
acceleration with great accuracy and confirmed the foregoing
results.
Now the lunar acceleration having been incontestably esta-
blished, it was an object of great interest to ascertain the cause
of this inequality. Euler came to the conclusion that it could
not be produced by the force of gravitation. Lagrange at a later
period demonstrated that neither the figure of the Moon, nor
that of the Earth, nor the direct attractions of the planets,
could be the cause of the phenomenon.
To give an idea of the position of the question when it was
* It is generally stated that Mayer employed in his Tables the coefficient
7" for the lunar acceleration, but M. Delaunay informs me that 6"' 7 was
really the co-efficient used by Mayer.
See Add. a la Conn, des TempSf 1864, p. 26.
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on presenting the Gold Medal to Prof. Adams, 1 6 1
attacked by Laplace, I may quote from his Exposition du
Si/stems du Monde,* the following remarks, slightly para-
phrased : — " This subject has much occupied the attention
of geometers, but their researches were for a long time un-
fruitful, not having led to the discovery of any cause which
could alter the Moon's mean motion, whether by the action of
the Sun and planets on the Moon or in consequence of the
non-spherical ^gures of the Moon and the Earth ; some astro-
nomers have in consequence come to the conclusion that the se-
cular acceleration had no existence ; others, in order to explain
it, had recourse to divers hypotheses, for instance, the action of
comets, the resistance of the ether, and the successive transmis-
sion of the force of gravitation. But the accordance of other
celestial phenomena with the theory of gravitation is so perfect,
that it could but be seen with regret that the secular acceleration
of the Moon should refuse allegiance to this theory, and thus
alone constitute an exception to a simple and general law
I which by the magnitude and variety of the objects which it
embraces does so much honour to the human intellect."
After many unsuccessful attempts to account for this phe-
nomenon, Laplace at last succeeded in mastering the difficult
problem, which had baffled so many distinguished mathema-
ticians and had escaped the sagacity of Lagrange, who (says
I M. Delaunayf ) " had almost touched it with his finger in his
I investigation of the Secular Variations of the Mean Motion
^ of the Planets" inserted in the Memoirs of the Academy of
I Berlin, 1783.
Laplace communicated his discovery to the Academic des
I Sciences ofPtLTis on the 19th November, 1787. In the Exposi-
tion du Sy Sterne du Monde ^ he thus states the cause of the
I secular acceleration : — " The secular equation of the Moon is
\ due to the action of the Sun on this satellite, combined with
the secular variation of the excentricity of the terrestrial
orbit:'
In accounting for the secular acceleration of the Moon,
I Laplace only took into account directly, the radial component
of the disturbing action of the Sun, which, as you know,
tends, on the whole, to dilate the lunar orbit. This force, it
will be remembered, does not affect the areal velocity of the
i Moon, but it does the angular velocity. Its effect is greater
! when the Earth is in perihelion than when it is in aphelion, so
that the Moon's orbit is more dilated when the Earth is in
perihelion ; it follows that, the description of the areas re-
maining the same so far as this central disturbing force is
concerned, the angular velocity is less and the lunar month is
consequently longer in our winter that in our summer. This
• Fifth Edition, vol. ii., pp. 75, 76.
t Addit. a la Conn, des Temps^ 1864, p. 39.
X Fifth Edition, voLii , p. 76.
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1 62 The Presidents Address
alternate dilatation and contraction of the lunar orbit, as you
know, gives rise to the annual equation. The mean dimi-
nution of the Moon's angular velocity, caused by the radial
disturbing force, depends, in some degree, on the excentricity
of the Earth's orbit, and is greater or less according as that
excentricity is greater or less. Hence if the excentricity of
the Earth's orbit diminishes, the Moon's angular velocity will
increase.
Now among the changes in the elements of the Earth's orbit
produced by the attraction of the planets, there occurs this
change of excentricity, which is the cause of the lunar accel-
eration ; the semi-major axis of the Earth's orbit, or the Earth's
mean distance, undergoes no permanent alteration, but the ex-
centricity of the Earth's orbit ia always varying ; for ages it
has been gradually becoming less, and according to Lever-
rier* will continue to do so for about 23,980 years from 1839,
when it will have attained a minimum value of 0*003314, after
which it will again increase, until it attains its maximum.
As the excentricity of the Earth's orbit becomes less each
succeeding year the Earth and Moon will not approach so close
to the Sun at the epoch of perihelion as in the preceding
year, and the Moon's orbit will gradually contract, and conse-
quently her angular motion will increase. Laplace says, " The
action of the Sun on the Moon diminishes by-ji^th her angular
velocity, and the numerical coefficient of this diminution of the
angular velocity varies inversely as the cube of the distance of
the Sun and Earth. Now in developing the inverse cubic power
of the distance in a series arranged with regard to the sines and
cosines of the mean motion of the Earth and its multiples, the
semi-major axis of the orbit being taken as unity, it is found
that this series contains a term equal to three times the half
of the square of the excentricity of the Earth's orbit; the
diminution of the angular velocity of the Moon contains the
product of this term by -j-fgth of this velocity. This product
would be confounded with the mean angular velocity of the
Moon, if the excentricity were constant ; but its variation,
though small, has an influence in the long run on the lunar
motion. It is evident that it accelerates this motion when
the excentricity diminishes." Ultimately this acceleration will
in the course of ages cease, and the Moon's mean angular
motion will then begin to decrease.
Laplace further pointed out that the motions of the lunar
perigee and nodes were subject to secular inequalities dependent
on the same cause as the lunar acceleration. He also proved
that the Moon's orbit has always the same mean inclination to
the ecliptic, and that the changes produced in the excentricity
and major axis of the lunar orbit, by the change of excentricity
of the Earth's orbit, are insensible.
* Additions a la Connaiasance dea Temps, 1843, P* 47-
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on Presenting the Gold Medal to Prof. Adams. 163
Laplace found that the lunar acceleration amounted to
11"' 1 35 in a century, though, in consequence of taking into
account a modification of the masses of Mars and VenuSy upon
which the rate of decrease of excentricitj of the Earth's orbit
in a great measure depends, he subsequently reduced this quan-
tity to 10"* 1 8. But in carrying back the calculations of the
Moon's place to the period of the Chaldean observations he
found that it was necessary to introduce a new term depending
on the cube of the time,* so that if t denoted the number of
centuries from the assumed epoch, the acceleration would be
io"-i8i6 t" + o"-oi854^'.
The value assigned by Laplace for the lunar acceleration
accorded fairly f with ancient eclipses and modern observa-
tion, and it is a fortunate circumstance that, at the period it was
published, it did so, otherwise grave doubts might have
arisen as to the sufficiency of the theory of gravitation to ac-
count for the phenomenon then under anxious consideration.
Subsequently in 1820, in consequence of the powerful
impulse of the Acadimie des Sciences of Paris, J the theory
of the Moon was again investigated by M. Damoiseau, and
also by MM. Plana and Carlini. They carried their approxi-
mations to a much higher order than Laplace had done, but
they failed to discover that the tangential force also produced
a permanent secular effect. Their investigations did not greatly
change the coefficient arrived at by Laplace (io"-i8i6).
Plana's value was io"'58 in a century, whereas M. Damoiseau,
by calculating directly this coefficient in a numerical form, ar-
rived at the number 10" 'jz.
These new values for the secular acceleration of the mean
motion of the Moon did not materially alter the times computed
for the ancient eclipses, so that Laplace rested perfectly satisfied
with the results of analysis, and was not induced therefore to in-
vestigate rigorously all the effects which would be produced
by the Sun's disturbing force. With respect to the theory
which ascribed the acceleration of the Moon's mean motion to
the resistance of the ether in space or to the progressive trans-
mission of the force of gravitation, he thus disposes of these
hypotheses : " When only the acceleration of the mean motion
of the Moon was known, it might have been attributed to the
resistance of the ether, or to the successive transmission of the
force of gravitation. But analysis shows us that these two
causes cannot produce a sensible alteration in the mean mo
* Expositum du Syathne du Monde, 5th edit., yol. ii., p. 76.
t The accordance was not perfect, as will be seen by an examination of
the Table inserted by M. Delannay in the Add. a la Conn, det Tempsy 1864,
p. 29.
% At the instigation of Laplace the Academy of Sciences of Paris made
the Lunar Theory the subject for competition for the Grand Prize of Mathe-
Digiti
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164 The Presidents Address
tions of the nodes and perigee which I have shown to depend on
the same cause as the secular acceleration."
He goes on to say that the accordance between theory and
observation in respect of the secular acceleration establishes
with certainty the constancy of the length of the day ; "for if
the length of the day were greater now by the one-hundredth
of a second* than in the days of Hipparchus, the actual dura-
tion of a century would be greater by 365*25 seconds, during
which time the Moon describes an arc of 17 3"* 2: the mean
secular acceleration of the Moon would in consequence be
increased by 4"' 3 8 for the first century, from the year 1801; a
quantity not admissible by theory." Of course if the accord-
ance between theory and observation, thus supposed by Laplace,
does not exist, this reasoning of his falls to the ground; and it
will presently be seen that M. Delaunay has recently from
other considerations arrived at the conclusion that the sidereal
day has actually lengthened.*
M. Hansen was the next to take up the question, he cal-
culated the coefficient of the secular acceleration of the Moon
on several occasions, and found in the first instance 1 1"*93
{Astrotwmische Nachrichten, No. 443, March 1842), which
he afterwards reduced to 11 "'47 (No. 597, May 1847).
Such was the state of the theory when Mr. Adams, in a
Memoir read before the Royal Society of London on the i6th
of June, 1853, and published in the Philosophical Transactions
for the same year, pointed out an important error in the method
pursued by MM. Plana and Damoiseau in obtaining the secular
acceleration of the Moon. The correction of this error in-
volved a considerable diminution in the theoretical value of
this acceleration. The object which Mr. Adams proposed to
himself in this Memoir was to determine the amount of the
acceleration of the Moon's mean motion which was due to the
cause assigned by Laplace. The problem which he undertook
to solve may be accordingly stated in the following purely
mathematical form. If the Earth be supposed to describe about
the Sun an elliptic orbit, the excentricity of which varies
slowly and proportionally to the time, while the other elements
remain constant, what will be the change in the Moon's mean
motion due to this change of excentricity of the Earth's orbit.
In the introduction to his Memoir, Mr. Adams thus briefly
explains the principle of the method employed by Laplace in
the solution of this problem: —
" It is readily shown that the mean central disturbing
force of the Sun, by which the Moon's gravity towards the
Earth is diminished, depends not only on the Sun's mean dis-
tance, but also, in some degree, on the excentricity of the
Earth's orbit. Now this excentricity is at present and for
many ages has been diminishing, while the mean distance re-
* See page 174.
Digiti
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on Presenting the Gold Medal to Prof, Adams. 165
maiDB unchanged. In consequence of this, the mean disturbing
force of the Sun is also diminishing, and therefore the Moon's
gravity towards the Earth at any given distance is, on the
whole, increasing. Also the area described by the Moon about
the Earth is not affected by this alteration of the central force,
whence it may be readily inferred that the Moon's mean dis-
tance from the Earth will be diminished in the same ratio as
the force at a given distance is increased, and that the mean
angular motion will be increased in double the same ratio."
In the Mecanique Celeste, the approximation to "the value
of the acceleration is confined to the principal term, which
depends on the first power of the Sun's disturbing force.
In the theories of Damoiseau and Plana, a great extension
is given to the theory of Laplace by taking into account the
square and higher powers of the disturbing force, but the
principle of the methods by which they determine the value
of the acceleration, may be regarded as essentially the same as
that of Laplace's method, which has just been explained.
Now, it will be observed that the reasoning employed in
this method is founded on the supposition, that the area
described in a given time by the Moon about the Eaii;h un-
dergoes no permanent alteration, or, in other words, that the
tangential disturbing force produces no permanent effect. If
we confine our attention to the first power of the Sun's dis-
turbing force, as Laplace has done, this supposition holds
good, but if we proceed to take into account the square and
higher powers of the disturbing force, the same supposition is
no longer strictly true.
In Mr. Adams' Memoir he endeavours to point out, in
popular language, the manner in which the inequalities of the
Moon's motion are modified by a gradual change of the mean
central disturbing force, so as to give rise to a permanent
alteration of the mean areal velocity of the Moon about the
Earth.
As an example, he takes the inequality called the varia-
tiony which is the most direct effect of the disturbing force.
In the ordinary theory, the orbit of the Moon, as affected
by this inequality only, would be symmetrical with respect to
the line of conjunction with the Sun, and the areal velocity
generated while the Moon was moving from quadrature to
syzygy would be exactly destroyed while it was moving from
syzygy to quadrature, so that no permanent alteration of areal
velocity would be produced.
In reality, however, the magnitude of the disturbing force
by which this inequality is caused depends in some degree on
the excentricity of the Earth's orbit, and as this is continually
diminishing, the central disturbing forces at equal angular dis-
tances on opposite sides of conjunction will not be exactly
equal. Hence the orbit will no longer be symmetrically
situated with respect to the line of conjunction. Now the
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1 66 The Presidents Address
change of areal velocity produced by the tangential force at
any point depends partly on the value of the radius vector at
that point, and consequently the effects of the tangential force
before and after conjunction will no longer exactly balance
each other.
The other inequalities of the Moon's motion are simi-
larly modified, especially those which depend more directly on
the excentricity of the Earth's orbit, so that each of them gives
rise to an uncompensated change of the areal velocity.
The distortion in the form of the Moon's orbit, which is
thus produced by the continual alteration in the excentricity
of the Earth's orbit, is of the order of the Sun's disturbing
force. Hence the alteration of the tangential disturbing force
due to this distortion will be of the order of the square of the
Sun's disturbing force. And, since this alteration of the tan-
gential force is the only cause which produces a permanent
change in the Moon's areal velocity, it follows that the rate of
change of the mean areal velocity will also be of the order of
the square of the Sun's disturbing force.
It is evident that this change of the Moon's mean areal
velocity will give rise to a change of the same order in the
amount of the lunar acceleration.
After giving this general reasoning in the introduction to
his Memoir, Mr. Adams proceeds to the strict mathematical
treatment of the problem.
For the sake of simplification he confines his attention to
the terms which are independent of the excentricity and in-
clination of the Moon's orbit, and which do not involve any
higher power o£m than the fourth — m denoting, as usual, the
ratio of the Sun*s mean motion to that of the Moon.
He arrives at the conclusion that instead of the secular
equation contained in Plana's expression for the true longitude
in terms of the mean, namely,
the following secular equation should be substituted
The principal term of the correction to be applied to Plana's
value of the secular acceleration is therefore
And as the value of the integral
Digiti
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on Presenting the Gold Medal to Prof. Adams. 167
/(e'« - £'=») ndt^- i27o'Y-p-Y nearly
where t is expressed in years, the numerical value of this
term is
Of course it might be expected that the succeeding terms
of Plana's expression for the secular equation would also be
materially changed.
It was not till 1856 that this important Memoir of Pro-
fessor Adams* attracted attention, when M. Plana himself was
induced by it to re-examine a portion of his Theorie du
Mouvement de la Lune. In a paper published in April of
that year, he admitted that his theory was imperfect, and he
deduced Mr. Adams' result from his own equations. Soon
afterwards, however, M. Plana retracted his admission of the
correctness of Mr. Adams' result, and obtained another result,
differing both from that which he had originally found,, and
also from that of Mr. Adams.
In 1857 Professor Hansen's valuable work, entitled Tables
de la Lune, was published. In this work the coefficient 1 2"' 1 8
was adopted for the secular acceleration of the Moon's mean
motion.
M. Delaunay in 1859 undertook the investigation of this
part of the lunar theory, and in the first instance carrying the
calculation as far as the term involving m^, he found exactly
the same value for this term as Mr. Adams had done, namely
—^ m^. This result was communicated to the Academy of
Sciences on the 17th January, 1859. ^^ being informed of
this, Mr. Adams immediately published the values which he
had some time previously obtained for the terms involving m^,
m\ and m^ (Academie des Sciences de Paris, 31 January,
1859, Monthly Notices, April 8, 1859*). (This paper con-
tained an erroneous coefficient, which was subsequently cor-
rected. It arose from writing ^^^^ ^^ m^, instead of ^^^\o^ ^^
and was therefore simply a clerical error.) The result of
Mr. Adams' new investigation was to reduce the coefficient
of the lunar acceleration to 5 "7, or about half the value hitherto
received. In a supplement to this paper f Mr. Adams
communicated the values of the two principal terms in the
expression of the lunar acceleration, which depend on the
excentricity and inclination of the orbit. He found that the
* Monthly Notices, vol. xix., p. 207.
t Ibid. p. 208.
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i68 The Presidents Address
term in c* increases the coefficient of the acceleration by
o"*036, while the term in y* diminishes it by 0*097, so that
this coefficient is ultimately reduced to 5" 64. I call atten-
tion here to a remark of Mr. Adams, which was expanded in a
subsequent communication into a fuller anticipation, that ano-
ther cause besides gravitation was concerned in producing the
lunar acceleration. He says that he believes the value just given
to be within one-tenth of a second of the true theoretical value of
the coefficient of the secular acceleration, and adds, " Whether
ancient observations admit of such a small value of the acceler-
ation is a different question." M. Delaunay, on the 25th April,
1859, communicated to the Academie des Sciences the result
of a more elaborate investigation, wherein he confirmed all the
new terms of Prof. Adams just alluded to, and, by carrying
the approximation to the eighth order, fixed the lunar ac-
celeration at 6"' 1 1 in a century.
It was after the publication of the foregoing results that the
controversy commenced which occupied so much of the atten-
tion of physical astronomers. The propriety of introducing
the new terms developed by Mr. Adams was called into ques-
tion by M. de Pontecoulant {Accuiimie des Sciences, 30 May,
1859), and, under date of the 28th of the same month, this
distinguished mathematician communicated a note on the same
subject to the then President of our Society (Rev. R. Main)*.
In a letter from Prof. Hansen f to the Astronomer Royal, May
21, 1859, attention is called to those three values at which he
had arrived at different periods, and which I have before
enumerated (see pages 164 and 167). With the solicitude which
he has invariably evinced for the interests of astronomy, Mr.
Main undertook the examination of the question, and com-
municated to the Society J an elaborate paper "On the
Present State of the Controversy respecting the amount of
the Acceleration of the Moon's Mean Motion," wherein he
clearly and fairly stated the bearings of the points under
dispute, and thus narrowed the field of controversy — " It is in-
cumbent on the opponents of Mr. Adams to show clearly that
the tangential force, producing alterations of the areal velocity,
can produce no effect on the secular acceleration." He at that
early stage stated that " Adams and Delaunay seem to have
right on their side." " But if we accept Mr. Adams's value of
the coefficient, and the principles of his investigation be estab-
lished beyond controversy, as in my own mind I have very little
doubt they will be, this value is far too small to satisfy the
ancient eclipses, and therefore some other cause (such as a re-
sisting medium) totally different from the disturbing influences
* Monthly Notices, vol.zix., p. 135.
t Ibid. p. 236.
t Ibid p. 268.
Digiti
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on Presenting the Gold Medal to Prof. Adams, 1 69
of the Sun and planets, must be resorted to, or we must hope,
from a hint dropped by M. Delaunay at the end of his paper,
that he has some means, at present kept out of sight, for laying
the ghost he has helped to raise."
In the Monthly Notices for April i860, vol. xx. p. 225,
Mr. Adams published his " Reply to various objections*' which
have been brought against the theory of the secular variation
of the Moon's mean motion.*
In this paper he calls attention to the fact that the question
under consideration is a purely mathematical one, with the
decision of which observation has nothing whatever to do.
If, as seems probable, ancient observations should show
that the Secular Variation of the Moon's Mean Motion is differ-
ent from that which, according to theory, would be produced
by the known change of the excentricity of the Earth's orbit,
it would be necessary to draw the conclusion that the mean
motion of the Moon is affected by some other cause or causes^
besides the variation of the excentricity which has been taken
into account, Mr. Adams remarks that '* this fact, if esta-
blished, would be a most interesting one, and might put us on
the traces of an important physical discovery."
It has been already mentioned, at the outset of these re-
marks, that the object of Mr. Adams' investigations was to
find the effect on the Moon's motion of a slow, uniform change
in the excentricity of the Earth's orbit, while the other ele-
ments of that orbit were supposed to remain constant.
Of course, in nature, the change of excentricity of the
Earth's orbit cannot take place without being accompanied by
changes in the other elements of the orbit, and in addition to
the secular change of excentricity there will be other changes
which are periodic.
If any part of the lunar acceleration could arise from such
changes of the elements as those which have just been men-
tioned, of course this part would not be given by Mr. Adams'
theory, which only professes to determine what amount of
acceleration is due to the regularly progressive diminution in
the excentricity of the Earth's orbit. If it should turn out to
be true that the acceleration is partly due to such periodic
changes in the elements of the Earth's orbit, this would in no
way be inconsistent with Mr. Adams' result.
In the paper last cited, Mr. Adams points oat that he has
made no assumption in his Memoir of 1853 respecting the
variability of the Moon's mean areal velocity. He proves
mathematically that this areal velocity does vary and finds
the amount of its variation, and the general reasoning given in
the introduction is simply the translation, so to speak, of his
analysis into ordinary language, in order to make the nature
of his correction to Plana's theory more generally intelli-
gible.
* See Appendix A.
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1 70 The President's Address
He remarks, too, that even if he had started with the
assumption that the mean aroal velocity was variable, no error
could have been caused thereby, for if this areal velocity had
been really constant, he would have simply found its va-
riation equal to zero. In mathematical language, the terms
constant and variable are not looked upon as exclusive of
each other, but a constant is regarded as a particular case
of a variable quantity.
Mr. Adams also states that in his investigations made sub-
sequently to his Memoir of 1853, he employed a new method
in which his results are obtained without taking into consider-
ation the mean areal velocity at all.
It was suggested by M. Hansen, that the difference be-
tween his value of the secular acceleration and that obtained
by M. Delaunay and Mr. Adams, might arise from a want of
convergency in the series proceeding according to powers of m,
by means of which they determine the coefficient of the
acceleration.
In order to remove all possible objection, Mr. Adams cal-
culated the value of that part of the coefficient of the accele-
ration which is independent of the excentricity and inclination
of the Moon's orbit, by a method which does not require any
expansion in powers of m, and the resulting coefficient
exactly agreed with that which he had previously found by
means of the series.
It would be needless to reproduce here the various argu-
ments which were used to show that Mr. Adams was wrong
in taking into consideration the variability of the areal velocity
of the Moon, or to make any further reference to the ob-
jections brought against the principles on which he had
conducted his investigations, because ultimately his results,
and consequently those of M. Delaunay, were confirmed
by the independent investigations of several mathematicians.
For example, by the late Sir John Lubbock,* who used in this
investigation formulae which he had before employed in re-
calculating many of the inequalities of the Moon's motion.
This distinguished mathematician, who contributed so greatly
to the development of the lunar theory, arrived at precisely
the same value for the much-contested term in w»^ as Mr.
Adams had done in 1853.
Professor Donkin, in a communication read June 14th, 1861,
and published in the Monthly Notie€s,1[ gave the results of an
investigation of the coefficient of m\ the calculation of which
involves the whole mathematical question of the subject then
under dispute. He used the same method of the variations of
elements which had been employed by M. Delaunay ; but as he
* Mem. Asi, Soc. vol. xxx. pp. 38-52, " On the Lunar Theory," read
November 9, i860.
t Vol. XXi. p. 241.
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on Presenting the Gold Medal to Prof. Adams. 1 7 1
had not had the opportunity of seeing what M. Delaunay had
published, his result may be regarded as independent testimony
of the correctness of Mr. Adams' value for that term.
Professor Cay ley,* by following a totally different method
from any used previously, also undertook the calculation of the
coefficient of »i*, and completely confirmed Mr. Adams' value.
M. Delaunay had previously, by two entirely different
methods, also arrived at the same value as Mr. Adams.
Baron Plana had, in 1856, as I have before stated, recog-
nised the correctness of Mr. Adams' value for the coefficient
of m^i but subsequently, in a paper read before the Academy
of Sciences of Turin, in June 1856, he retracted that admis-
sion, having arrived at a new result by a subsequent inves-
tigation. Ultimately, in 1 860, after repeating liis doubts as to
the correctness of Mr. Adams' coefficient for »i^, he,f in a
correspondence with Sir John Lubbock, admitted the cor-
rectness of Mr. Adams' value.
In these numerous confirmations of the correctness of the
result of Professor Adams, the verifications were obtained by
different methods, in which the savants who employed them
did not start with the assumption either of a variability or of a
non- variability of the areal velocity ; and the calculations were
consequently made without regard to the areal velocity at all,
the variability or non -variability of the mean areal velocity
being in fact part of the problem to be determined.
After the thorough investigation which the problem of the
secular equation of the Moon's motion has received at the
hands of so many distinguished mathematicians, there can no
longer be any question as to the correctness of the value of tl.e
coefficient determined by Mr. Adams and M. Delaunay. But
here comes a difficulty which, however, in no way casts any
doubt on Mr. Adams' theory : it is this, that the coefficient
5"7, or 6"' 1 1, as M. Delaunay has made it by further deve-
loping the series, does not account for the amount of the
secular acceleration as shown by observation. It is perfectly
true, notwithstanding some uncertainty as to the actual date
and place of the ancient solar eclipses, and also as to the
correctness of the records of certain lunar eclipses, that Prof.
Hansen's value of the secular acceleration, namely 12"' 18,
accords better with these phenomena than the smaller number
6".
Mr. Hartwig, in the Astronomische Nachrichten, No. 1 241,$
gives the results of his calculations of Nineteen Lunar Eclipses
contained in the Almagest, by means of Hansen's Solar and
Lunar Tables.
He comes to the conclusion that the results, on the whole,
accord satisfactorily with Hansen's Tables.
* Abstract, Monthly Notices^ vol. xxii. p. 32 ; Paper in full, ib. p. 173.
t See Add. d la Conn, des Temps, 1864, p. 56.
t i860, p. 257. See Appendix B.
Digiti
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1 7 2 The Presidents Address
In the Berichte der K, Sachs. Gesellschaft zu Leipzig^
15 April, 1863, is contained a short paper by Prof. Hansen,
in which he states that as the value of the acceleration, as cal-
culated by Adams and Delaunay, is considerably— nearly 6" —
less than that employed in his Lunar Tables, such smaller value
(as he had shown in the Comptes Rendus^ t. 1., 1860*0) cannot
represent the ancient eclipses.* Assuming Adams and De-
launay's coefficient to be the correct acceleration due to the
change in the excentricity of the Earth's orbit, the deficiency
must be accounted for by other causes. That which most
naturally presents itself is a change in the length of the sidereal
day or period of the Earth's rotation; and he remarks that
Laplace's demonstration of the invariability of the sidereal
day depends on the very assumption that the acceleration i^
wholly accounted for by the change of the excentricity of the
Earth's orbit, and consequently must in the present question
be put aside, t He proceeds to show that the deficiency of
6" in the acceleration would be accounted for by the almost
infinitesimal increase of o»*oii97 in the length of the sidereal
day in the course of 2000 years. J He, however, goes on to say
that it is remarkable that the value of the acceleration as ob-
tained by himself should agree so well with observations with-
out the assumption of any such supplemental cause.
In the second part of Hansen's Darlegung der theoretischen
Berechnung, ^c.y which has recently appeared, he has recal-
culated the secular variation of the mean longitude, and has
found the coefficient 12"'557. It has been pointed out to me,
however, that in his investigation he appears to have fallen
into an error of the very same nature as that of Plana and
Damoiseau to which I have already alluded. It is true that
in the passage in Art. 219 Prof. Hansen professes to have
already taken account of the terms to which Mr. Adams
called the attention of astronomers, but notwithstanding this
it would appear that he entirely neglects the non-periodic
term which the terms referred to will introduce into the
expression of the Sun's tangential disturbing force.
In fact, in the paragraph commencing at the foot of page 3
and ending at line 12, page 4, Prof. Hansen expressly states
that his calculation of the secular acceleration proceeds on the
assumption that K = o, or in other words that this term has
no secular variation.
Now since
* Abstract, Monthly Noticetj vol. xxili., p. »io.
t See the quotation from Laplace, page 164.
X Hansen's Darlegung j part i, art. %%y p. 332.
Digiti
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on Presenting the Gold Medal to Prof. Adams. 173
this is equivalent to assuming that -^ has no secular variation,
or that the Moon's mean areal velocity has no secular variation,
since the quantity which Hansen denotes by h is inversely pro-
portional to the areal velocity.* Accordingly, in part ii. Art.
305, p. 339, the value found for A ^ contains no non-periodic
term, and the terms which would have naturally led to the
introduction of such non-periodic term are expressly neglected,
because they would produce an effect on the element H, whereas
it is assumed that, in the calculation of the secular acceleration,
this element may be put = o. This, at all events, would
appear to be implied by the passage near the beginning of
Art. 305 : " Und lasst dabei die Glieder, die kein t ausserhalb
des Cosinuszeichens haben, weg, die spdter nur in dem Ele-
ment S Wirkung dussern konnen^und daher zufolge *der An-
nahme S =: o in Bezug auf die Sdculardnderung der mit-
tier en Ldnge hier wirkungslos bleiben.^* The only reason for
this assumption that H = o, which Prof. Hansen mentions in
the passage at page 4 of his 2d part above referred to, is the
agreement between his value of the secular acceleration and
that given by the ancient eclipses.f But it is evident that
the secular part of S should be determined by theoretical
considerations alone.
It is a purely mathematical process which leads to the
values of the quantities contained in H, and it is by the sub-
stitution of these values in this element that it must be deter-
mined whether S is equal to zero, or whether it has any other
value. It is evident that observation cannot decide whether a
mathematical process is correct or not, for the very question is,
whether the whole of the effect shown by observation is due
to the cause which has been taken into account in the mathe-
matical theory, or whether part of it may be due to some other
cause.
Indeed it now appears, from a letter which Professor Hansen
has done me the honour to communicate to me, under date of
Jan. 29 of this year, that some misapprehension has existed in
respect of the interpretation which has been put upon his
meaning hitherto, for he says, ^^I have never contested the
ideas of Mr. Adams in regard to the secular equation of the
* Hansen's Darlegung^ part i., p. 106.
f In Art* 298, p. 322 of the 2nd pM*t of the JDarlegung, M. Hansen
refers to his second memoir '* On the Perturbations of the Small Planets **
for a proof that B can contribute nothing to the secular variations ; but it
should be remarked that this' proof only takes into account terms which are
of the second order with respect to the disturbing forces, whereas the terms
which Mr. Adams has added to the Moon's secular acceleration are of the
third order with respect to the disturbing forces, since these terms are of the
the order of the square of the Sun's disturbing force multiplied by the
change of the ezoentricity of the Earth's orbit, and this change is itself of
the order of the disturbing forces of the planets on the Elarth.
F
Digiti
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174 ^^^ Presidents Address
Mood, but I could not make use of the coefficient derived from
his investigation, because it does not accord with observation.
It is an inevitable condition which must be fulfilled, in calcu-
lating tables of the Moon or the planets, that they represent
observations as far as possible. And if in any point the theory
does not satisfy this condition, we must change the corre-
sponding coefficient."* From this important explanation of Pro-
fessor Hansen, it becomes all the more necessary to fix the
dates and localities of ancient eclipses with the utmost attain-
able precision. For the attempts which have been made with
more or less success in this direction we are under great
obligation to Professor Hansen f himself, to the Astronomer
Royaljf to Prof. Hansteen,§ and among the pioneers in this
now increasingly important branch of inquiry, Mr. Bosanquet
must bft pUced in the foremost rank.||
Thus the value of the lunar acceleration due to the change
in the excentricity of the Earth's orbit, which has been de-
termined by Mr. Adams and M. Delaunay, may be regarded
as established beyond all doubt, while at the same time it
seems incontestable that a larger value is required in order to
satisfy the ancient eclipses.
M. Delaunay has recently endeavoured to remove this diffi-
culty by showing that there is a physical cause in operation
adequate to explain the difference between the theoretical and
the observed values of the acceleration. In a memoir read
before the Aoademie des Sciences^ on the i ith Dec. 1865,^ he
developes the following proposition: — The disturbing forces,
to which are due the periodical oscillations of the surface of the
seas, by their action on the liquid protuberances to which they
give rise, tend to diminish the motion of the rotation of the
Earth, and thus produce a sensible apparent acceleration in
the mean motion of the Moon. — This communication is worthy
of the earnest consideration of all physical astronomers; and
although it is possible that immediate adherence may not be
given to M. Delaunay's theory, it is sure to command the
attention of those best qualified to discuss its merits.
That the tidal wave tends to cause a retardation of the
Earth's rotation has been pointed out by Dr. J. R. Mayer, of
Heilbronn, in his Celestial Physics^ 1 848 ;** and this action of
* See Appendix D.
t Hansen's Darlegung, 2nd part, pp. 386, 392, 398. See also Ap.
pendiz C.
X Phil. Trans. 1853, Mem, R. A. Soc. 1858.
§ Ergdnzungs-H^ to the Astron. Nach.f published in 1 849.
{{ See Appendix E.
If Comptes RendWt tomelxi. Seance dn 11 Dec., 1865 : — see also Abstract
Month. Not. vol. xxvi. p. 85.
** Beitrdge zur Dynamik des HimmelSt in Populdrer Darstellung.
Heilbronn, 1848. Translated hj Dr. H. Debus, Phil, Mag.y fourth series,
1863, vol. xzv., p. 403.
Digiti
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on Presenting the Gold Medal to Prof. Adams. 175
the Moon has been made familiar to the English public by
Dr. Tyndall's Lectures on Heat.
It is not my intention to enter upon the merits of the Memoir
of M Delaunay in this address, but I deem it right to point
out that while Mayer and others have seen that the tidal wave
must act as a sort of brake tending to retard the rotation of
the Earth, this illustrious French mathematician is the first who
has attempted to prove that the effect is an appreciable quantity,
and such as could account for that part of the lunar accele-
ration which is not produced by the secular change in the
excentricity of the EartKs orbit This is a grand result, and
if confirmed, it must be ranked amongst the most important
contributions to astronomical physics.
The secular change in the excentricity of the Earth's
.orbit, although of long period, is, after all, periodic, and
hence that part of the acceleration of the Moon's mean motion
which is dependent upon it is also periodic. This is not the
case in respect of that part (the apparent acceleration) which
arises from the increase of the time of the Earth's rota-
tion, for that part will go on accumulating for ever ; countless
ages will, however, pass away before the length of the day
will be so altered as to change in an appreciable degree the
conditions of things upon the Earth. But the exact calculation
of the effect of the tides in retarding the Earth's rota-
tion is fraught with such great difficulties that it is most
probable that its amount will be best obtained by comparing
the whole observed amount of the lunar acceleration with that
part of it which is theoretically computed from the refiex action
of the planets, the primary effect of which is to change the
excentricity of the Earth's orbit.*
We thus see that the re-examination of Laplace's theory
of the Secular Equation by Mr. Adams has indirectly led
to a more formal investigation of how far the effect of the Sun
and Moon on the protuberance of the great tidal wave may
produce a retardation of the Earth's rotation equivalent to the
difference between Hansen's coefficient 12''* 5 5 7, and Adams'
and Delaunay's value 6"- 1 1 .
It should be observed that the question of what part of
the acceleration is real and due to the Sun's action, and what
part is merely apparent and due to a change in the time of
the Earth's rotation, is by no means without practical import-
ance.
For the part of the acceleration due to the first of the
above-mentioned causes is peculiar to the Moon, whereas the
part due to the other cause affects the places of all celestial
bodies in proportion to their angular velocities. Thus, if
the change in the time of the Earth's rotation produces an
* See Appendix F.
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1 76 The Presidents Address
apparent acceleration of 6" in a century in the motion of the
Moon, the same cause must produce an acceleration of nearly
o"'5 in a century in the motion of the Earth (or in the appa-
rent motion of the Sun), and nearly 2'^ in a century in the
heliocentric motion of Mercury.
I have now to speak of very important investigations
of Professor Adams', in respect of the Moon's Parallax^
Though I do not claim for these researches the same origin-
ality of ideas and method which characterised the memoir on
the Secular Acceleration of the Moon's Motion, yet they are
the representatives of a vast amount of labour, and are in the
highest degree creditable to the sagacity and industry of the i
author. ^
It is needless for me to dilate on the importance of an
accurate knowledge of the lunar parallax, for no observation
of the Moon's place can be compared with the theoretical
place as derived from the tables, without a previous re-
duction, wherein the question of the amount of parallax has
first to be taken into consideration. Mr. Adams, in examin*
ing Burckhardt's Tables, found that those relating to the lunar
parallax were defective.
The principal results of Mr. Adams' investigations respect-
ing the Moon's parallax are contained in a paper " On new
Tables of the Moon's Parallax, to be substituted for those of
Burckhardt," which was published in the Supplement to the 1
Nautical Almanac for 1 856,* and in another paper, " On the
Corrections to be applied to Burckhardt's and Plana's Parallax
of the Moon, expressed in terms of the Mean arguments," which
appeared in the Monthly Notices of the R, A, S., vol. xiii. p.
262.
Mr. Adams' attention was called to the discrepancies be-
tween the values of the Moon's parallax, as calculated from
the Tables of Burckhardt and of Damoiseau, by reading Mr.
Henderson's paper on the Constant of Lunar Parallax in the
tenth vol. of the Memoirs of the R. A. S. Mr. Henderson's
determination of this constant is based on thirty-four ob-
servations of his own, made at the Cape of Good Hope^ com-
bined with corresponding observations at Greenwich and .
Cambridge. The values of the parallax deduced from the 1
observations are compared with those calculated by means of
the Tables, both of Burckhardt and of Damoiseau.
Now it is remarkable that the values of the constant of
parallax thus found differ by i"*3, according as one set of
Tables or the other is employed in the comparison. Not
knowing which of these values to prefer, Mr. Henderson
adopts the mean of the two for his final result. A little con<-
sideration, however, will suffice to show the unsatisfactory
* Mr. Adams' Tables of tke Moon's Parallax have been reprinted in the
Addit. a la Conn, des Temps for 1856, and also in the Berliner Jahrbach for
the same year.
Digiti
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on Presenting the Gold Medal to Prof. Adams. 177
nature of this mode of procedure. It is to be remarked that
the onlj part of the investigation which is dependent on the
Tables consists in the reduction from the actual values of the
parallax at the times of observation, to the constant or the
mean value of the parallax. Now it is plain that so lai^e a
difference as i''*3 in the mean amount of these reductions cor-
responding to the thirty-four observations concerned, can only
arise from intolerable errors in the periodic terms of the paral-
lax given by one of the two sets of Tables. The two results
musty therefore, be regarded as contradictory of each other,
and must not be combined together. One of the results may
be good, but if so, it is sure to be vitiated by combination
with the other which must be decidedly erroneous.
Damoiseau's Tables give the parallax at once in the
form in which it is furnished by theory, but the expression
of the parallax which is used in Burckhardt's Tables is adapted
to his peculiar form of the arguments, and requires transforma-
tion in order to be compared with the former. When this trans-
formation had been effected, Mr. Adams found that several of the
minor equations of the parallax deduced from Burckhardt differed
essentially from their theoretical values given by Damoiseau.
With regard to the parallax, Burckhardt professes to have
followed the theory of Laplace, but as this agrees very closely
with that of Damoiseau, it is clear that errors must have
crept into Burckhardt's transformation of Laplace's formula.
These errors appear to have arisen in the following nianner.
In the formation of Burckhardt's arguments of evection
and variation, the mean longitude of the Sun is employed.
Now, four of the errors in the coefficients of the minor equa-
tions may be accounted for, by supposing him to have erro-
neously employed the true instead of the mean longitude of
the Sun in forming the above-mentioned arguments. In
another of the minor equations, the coefficient is taken with
a wrong sign, and in another a wrong argument is employed.
On further inquiry, Mr. Adams discovered that the differ-
ence between Burckhardt*s equations of parallax and those of
Burg and Damoiseau had been long since remarked by Clausen
in a valuable comparative analysis of the three sets of lunar
tables given in the 1 7th volume of the Astronomische Nach"
richtefiy but this remark seems to have excited no attention
whatever.
After examining Burckhardt's Tables of Parallax, Mr.
Adams was naturally led to scrutinize more closely the results
of the theories of Damoiseau, Plana, and M. de Pont^coulant* in
relation to the same subject. Although the differences be-
tween the results of the several theories were, in general,
BmaJl when compared with the errors of Burckhardt, still
they were greater than we had a right to expect would ba'^e
been the case, considering the close agreement which existed
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178 The Presidents Address
between the several theories with reference to the equations
of longitude.
On examining the processes which had been employed by
the several authors, he found that the numerical values of the
coefficients of the equations of parallax assigned by them by no
means fairly represented the most accurate values of those co-
efficients which the several theories were capable of giving.
In the theories of Damoiseau and Plana, the expression for
the reciprocal of the projection of the Moon's radius vector upon
the plane of the ecliptic in terms of the Moon's true longitude,
is required in order to find the relation between that longitude
and the time, and consequently the utmost care has been taken j
to obtain that expression with accuracy. \
In the subsequent operations and transformations necessary
in order to deduce the expression for the parallax, first, in
terms of the Moon's true longitude, and finally, in terms of the
time, the same care has by no means been employed. In
Damoiseau's theory, the coefficients of the expression for the
reciprocal of the projected radius vector are only given nu-
merically, and the quantities neglected in the subsequent trans-
formations are not very important, although they are still
sensible. In Plana's theory, the coefficients of the same ex-
pression are given in their analytical form, and the approxima-
tions are carried to the seventh, or even to the eighth order of
small quantities, in cases where this degree of accuracy is i
requisite. In the transformations for finding the parallax, .
however. Plana neglects all quantities which are of higher !
orders than the fifth, and consequently many of his coefficients
are very sensibly in error.
In M. de Pontecoulant's theory, the time is taken as the in-
dependent variable, and the analytical expression for the parallax
in terms of the time is obtained immediately, and is developed
to as great an extent as the corresponding expression for the
longitude. In the conversion of his formulae into numbers,
he, however, neglects all the terms beyond the fifth order, and
therefore many of his coefficients, like Plana's, are senaibly
erroneous.
Mr. Adams has endeavoured to supply the defects and i
omissions in the several theories which have been above 1
pointed out. He has transformed anew Damoiseau's and
Plana's expressions for the reciprocal of the projected radius
vector, so as to obtain the expression for the parallax in terms
of the time, with all the accuracy of which the respective
theories admit, and he has also converted into numbers the
terms of M. de Pontecoulant's expression for the parallax
which have been neglected by M. de Pontecoulant himself.
In the course of these operations, Mr. Adams has succeeded
in detecting and tracing back to their sources a considerable
number of errors, especially in Plana's work, and has. thus
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on Presenting the Gold Medal to Prof. Adams, 1 79
been able to remove many of the discrepancies between the
results of Baron Plana and M. de Pontecoulant.
When the values of the parallax given by the several
theories had been corrected in the manner above described, the
agreement between them was found to be most satisfactory.
The difference between the separate values of each coefficient
of parallax and the mean of all, rarely amounted to a hundredth
part of a second.
As an example of the differences between the values of the
coefficients of parallax originally given by the several authors,
we may take the coefficient of the principal term in the varia-
tion inequality, the argument of which, expressed in Damoiseau's
notation, is 2 1,
The several values given for this coefficient are the fol-
lowing : —
//
Damoiseau ». .. 28*54
Plana .. .. 27*59
Pontecoulant ., .. * 7*4 7 5
whereas all the theories, when corrected, agree in giving the
value
28"-»3
In one of Plana's coefficients the error amounts to not less
than i'^*9y but this simply arises from the principal term in the
analytical expression of this coefficient having been inadver-
tently taken with a wrong sign, in the conversion of the for-
mula into numbers.
Mr. Adams has taken particular pains with the theo-
retical determination of the Constant of Parallax, and with
regard to this the agreement of the several theories is perfect.
From Dr. Peters' value of the Constant of Nutation, it may be
deduced that the ratio of the Earth's mass to that of the
Moon is as 81*5 to 1 very nearly. Employing this ratio, to-
gether with the dimensions of the Earth according to Bessel,
and the length of the seconds' pendulum in latitude 35|^,
deduced from Mr. Baily's Report on Foster's Pendulum Ex-
periments, he finds the value of the Constant of Parallax to
be 3422"*32 5.
This result agrees admirably with that found by Mr.
Henderson, in the paper cited above, when the observations
are reduced by means of Damoiseau *s Tables.
In the seventeenth volume of the Astronomische Nachrichten,
M. Hansen gave the value of the parallax which he had at
that time obtained by means of his new method of treating
the lunar theory. Mr. Adams transformed this expression with
great care, so as to compare it with the results of the former
tiieories. The agreement is in general very close ; the differ-
ence between the values of the co-efficients seldom exceeding
a hundredth part of a second.
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1 8o The F^endenU Address
There are onlj two instanoes in which the difference is
much greater than this quantity. One of these cases is that
of the Constant of Parallax, the yalae of which, given bj M.
Hansen's theory, is o"*o6 less than the corresponding value
found from the same fundamental data by the other theories.
The second case is that of the term whose argument ex-
pressed in Damoiseau's notation is i-^Zj the co-efficient being
o''*i46 according to Damoiseau and Plana, o"'i40 according to
Pontecoulant, and o'''i8i according to Hansen.
In both these cases Mr. Adams finds that Hansen's defi-
nitive values of the co-efficients as given in his Lunar
Tables differ sensibly from those given in the paper above
referred to, and agree closely with those which result from
the former theories.
In the formulas given in Mr. Adams' published papers on
Parallax, referred to at the beginning of this notice, quan-
tities less than o''*o5 have been neglected, except in cases
where they can be included in the same table with larger
terms. In Mr. Adams' computations, however, quantities far
smaller than this have been taken into account, and an addi-
tional place of decimals has been employed, beyond that re-
tained in the results.
The total error in the periodic terms of Burckhardt's Tables
of Parallax may amount to nearly 6", and independently of
this his constant of parallax requires an increase of nearly 2".
It is unfortunate that so erroneous a value of the Parallax,
as that of Burckhardt, should have been so long employed in
the Nautical Almanac^ and consequently should have been
used in the reduction of such a vast number of lunar observa-
tions.
In the Appendix to the Nautical Almcmac iov 1856, which
contains Mr. Adams' Tables of the Parallax, are also given
tables of corrections to be applied to the values of the
Parallax given in the Nautical Almanac, for every day in
each of the years from 1840 to 1855 inclusive* From 1856
to 1 86 1 inclusive, the values of the Parallax given in the
Nautical Almanac were computed by means of his tables.
Subsequently to that time Hansen's Tables have been em-
ployed.
In Mr. Airy's " Reductions of the Greenwich Lunar Ob-
servations," from 1750 to 1830, Plana's formula for the Pa-
rallax has been employed. We have already seen that this
formula requires corrections which are by no means insensible.
I could quote largely from my friend and a former occupier of
this Chair, the Rev. R. Main, in elucidation of the vast amount
of trouble which has been occasioned by the artificial arguments
which had been devised by Burckhardt in the construction
of his tables, but Mr. Main's lucid explanation of the claims
of that fine old veteran Hansen to your gratitude, are so
vivid in your recollection that it is needless for me to do so.
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on Presenting the Gold Medal to Prof. Adams. 1 8 1
The address which he delivered in 1 860 contains so much of
interest that it is worthy of re-perusal now that we are deal-
ing with the utmost refinements of the lunar theory. My own
experience has led to the opinion, often expressed, that a large
portion of time is taken up in the correction of errors, and this
remark most certainly applies to practical astronomy; most
grateful ought we, therefore, to be to those men who, with zeal
and untiring industry, occupy themselves in labours such as
those to which I have called attention, and who by their
sagacity have saved us from the uncertainty and useless toil
invariably entailed by the use of erroneous tables.
Besides the works before mentioned, there are several in-
vestigations by Mr. Adams, the results of which have been
published without the processes which have led to them ; and
it will not be considered out of place to direct attention to
these works, although they do not constitute any part of the
grounds on which the award of the Medal was made. One
of these is an investigation of the relative positions in space of
the two heads of Biela's Comet, as deduced by means of a
method of his own from the apparent relative positions ob-
served at Cambridge. This investigation showed that the
relative motion during a month might be fully accounted for
without supposing any sensible mutual action between the two
heads. The periodic time of the smaller head was found to be
8*48 days longer than the periodic time of the larger. The
results of this interesting investigation were published in the
Monthly NoticeSy vol. vii. p. 83 (April 1 846).
Among the works of Mr. Adams I find in the Nautical
Almanac for 1851, a correction to Bouvard*s Table XLII., of
Saturn, The re- examination of the theory of this planet was
suggested by the discordances between the computed and ob-
served places exhibited in the Greenwich Planetary Reductions,
No higher testimony to the practical value of this investiga-
tion is needed than to state that the results are now employed
by Mr. Hind in the computation of the places of Saturn for
the Nautical Almanac. ^
Another investigation involving considerable labour is that
relating to the mass of Uranus^ which will be found in the
Monthly Notices, vol. ix. p. 1 59. Two values of this mass
had been previously given, differing widely from each other.
Bouvard, from the action of Uranus on Saturn, found the mass
to be TTTT^ o^ '^® Sun's mass; while more recently, from
observations of the satellites, Lament obtained the value
Tf iu7' From a careful reduction of Mr. Lassell's observations
of the fourth satellite (which are more to be depended on for
this purpose than those of the second) Mr. Adams obtained
the value inriirT> which is almost exactly a mean between tha
results of Bouvard and Lament He also reduced all Sir Wm.
Herschel's measures of distance of the satellites, given in his
paper in the Phil. Trans. 181 5, and obtained from the ob-
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1 82 The Prendenfs Address.
servations of the fourth satellite the quantity ^,|gg , which
agrees closely with that found from Mr. Lassell's observations.
Mr. Adams arrived at the conclusion that ^^^(^(^ is probably
much nearer the true value of the mass than either of the
values that had been previously given, and that it may be
employed, provisionally at least, in the theory of Neptune,
without risk of any considerable error.
In Admiral Smjrth's ^des HartwelliamB, P- 34I9 ^^^ also
in his Speculum Hariwellianum, p. 364, are published Mr.
Adams' results respecting the orbit of the double star y Ftr-
ginis. The orbit given by Sir John Herschel, in the results
of his Cape ObservationSy was taken as the basis of the calcu-
lations ; and equations of condition for the correction of the
elements were formed, by comparing certain selected angles of
position deduced from observation with the values calculated
by means of Sir John Herschel's elements. These equations of
condition were formed by a method of Mr. Adams' own, which
appears to be more simple than any other before used.
Laplace has said, that every difficulty which has arisen in
explaining the inequalities of planetary movements has ulti-
mately served to establish on a firmer basis that most bril-
liant discovery of Newton, — the law of Universal Gravitation.
Among those ardent and illustrious mathematicians, who
have contributed towards the clearing away of these diffi-
culties, there is none who stands higher than the recipient
of the Medal this day, whose name is and ever will be
associated with that grand investigation of the perturba-
tions of UranuSj by an unknown planet, with which he
began his career. It does not come within the purpose of
my present address to enter upon the connexion of Professor
Adams with the discovery of the planet Neptune ; it would
suffice to say that those most competent to judge of the merits
of this celebrated investigation have always been greatly im-
pressed by the power and comprehensiveness with which, from
beginning to end, he grasps all the bearings of this difficult
subject, as well as by the clearness, directness of aim and
precision, which characterize his whole treatise : — but I cannot
refrain from recalling those memorable words uttered by Sir
John Herschel, who, in speaking of Leverrier and Adams in
connexion with that discovery, declared theirs to be " names
which Grenius and Destiny had joined," to " be pronounced
together so long as language shall celebrate the triumphs of
science in her sublimest walks."
And now. Professor Adams, it only remains for me to con-
gratulate you most heartily on the full confirmation which
your theory of the Secular Acceleration of the Moon's mean
.motion has received at the hands of so many distinguished
analysts, and in presenting you with this Medal to express a
hope that your health may long permit you to exercise that
great intellect with which you have been endowed, and which
you have so highly and so successfully cultivated.
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Appendix A.
(See Monthly Notices, vol. zz. oommencing at p. 230.)
In Mr. Adams' "Reply to Various Objections" he points ont that the
error of M. Plana's orig;inal value of the secular acceleration , given in his
*' Theorie du Mowement de laLwte,** arises from his assumption that one
of the so-called constant quantities introduced by integration is absolutely
constant, whereas it is really subject to a secular variation. He also shows
that the value of the accderaiiDn given by M. de Pont^coulant in the Compies
Rendna of April 9, i860, differing widely as it does from that of M. Plana, is
vitiated by an assumption of ezactly the same kind with respect to another
constant introduced by integration.
In M. Plana*s theory a constant is introduced which is denoted by h'.
In M. de Pont^ooulant's theory two constants are introduced, which are
denoted by h and - respectively.
These constants are not independent, but are connected with each other
and with the Moon's mean motion u by the following relations :—
in which formulae the sum of the masses of the Earth and Moon is supposed
to be unity, the excentricity and inclination of the Moon's orbit are neglected,
and powers of m above the fourth are omitted.
By differentiating these relations and observing that — -^ ■■ -rr since
^ -^ ^ fndi ndi
m n, which is the Sun's mean motion, is constant, we may obtain,
ndt ^hdi ^ di \ 2*"^ i»8 "• J
dn 3 da d(t^) i 3 „« . 5117«4 l
ndi %adi di (
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1 84 Appendix,
If r— ;- be neglected, or h be supposed to be constant, we obtain the
hat
value of -^-T found in M. Plana's theory.
ndt
If — r- be neglected, or a be supposed to be constant, we obtain the
aat
value of —r- found by M. de Pont^coulant, in his paper in the Comptes Ren-
nat
dtu above referred to.
If —3- be neglected, we obtain the value of -j-, which would have
A at flat
been found by M. de Pontecoulant, if be had siiqppoaed the quantity h to be
i^bsolutely constant instead of the quantity a.
dn
iTt
and the reason ia, that the quanties h^ K and a, are really variable, and
therefore ,— ?-;, -r-r^t and -— -, cannot be neglected. If the values of these
Yidt hat adi
differential coefficients be found in the way which Mr. Adams pmnts out, and
then substituted in the above equations, we find firom all alike the value
dn
ndt
di I a*" 64 >
which is the result obtained by Mr. Adams.
Damoiseau's value of the acceleration is not expressed in an analytical
form, but his method of obtaining it is exactly equivalent to that oi M.
PUna.
M. Hansen, as is well known, does not express the lunar inequalities in
terms of m, but, from the remarks which have been akeady made in this
Address respecting his method of finding the acceleration, it appears pro.
bable that his process ia equivalent to neglecting j-Ta ^^ assuming that the
quantity h is absolutely constant.
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Appendix.
185
Appendix B.
For the following tabular view of the results of Mr. Hartwig I am
indebted to Mr. Marth, who remarks that Nos. 15 and 19 are favourable to
Mr. Adams's acceleration, but that all the others are opposed to it. The
preyailing sign of the differences between the recorded and computed times
appears to favour a diminution of the coefficient for the secular acceleration
employed in the tables of about z". The necessity however of rendering
eclipse No. 8 physically possible (assuming that there is no error in the date)
aeema strongly opposed to such diminution.
Greatest Phase
Ne. Date. Place. Recorded. CaL
I — 720 March 19 BabykMi total i*<
2, — 719 March t „
3—719 Sept. I
4 — 620 April 2 1
5 — 521 July 16
6—501 Nov. 19
7 -490 April 25
— 424 Oct. 9
-412 Aug. 27
— 405 April 15
« -3S2Dec. 22 Bab^n
9 — 381 June 18 ,9
10 — 381 Dec. 12 „
1 1 — 200 Sept. 22 Alexandria
12 — 199 March 19 „
13 - 199 Sept. II
{Beg. a good hoar after )
moonrise (which oc- >
carred towards fi*). )
Cal.
Ti»e.
h m
7 8
Diflf.
4. C'2I 5" Middle uncertain, ) n fo
* ^^^ I about midnight. f ^
more than i 0-57 f Beg after mwnrise } 6 14
" ■" I (towards 6i>>). i
^ 0*07 Beg. 1 6*" 37" 15 56
0*4. p i Mid. uncertain, an } 11 3,
^•^ i hour before midnight. 3
Q.J J S* Hid. uncertain, aboat 1 n 24
r SUd. uncertain, abcfut ^ ^^ j.
B^.wkilehalfan )
hour of the night was } lo 53
. yet left (rt^* 31-). )
h m
Beg. 7 47
-41"
n
i
0-45
>f
i
o*ii
i»
i
0«02
Athens
total
1-34
Syraciae
»»
i-i^
Athens
»»
'•34
+ 22
total 1*42
total
total
14 - 173 April 30 „ ^
15 — 140 Jan. Ay Rhodes (
16 125 April 5 Alexandria J
17 133 May 6 „ total
i
18 134 Oct. so
19 136 March 5
i
1*44
1-65 [
067 I
0*29
O'll
ro5
o-8«
o*43
Beg. 9 36
End. 8 26
Beg. II 28
Beg. 12 36
Mid* 1411
Beg. 12 49
Mid. 15 32
Beg. 9 56
Mid. uncertain, about
Mid. II 8
Mid. 10 47
Mid. 16 13
25 —22
8 55 -41
7 57 -49
«o 54 -34
12 15 —21
}j» 15 — ai
14 6 - s
}
12 8 —41
14 50 -42
« 41 -75
} 839
10 41 —27
10 37 —10
15 29 -44
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1 86
Appendix.
Appendix C.
I am indebted to Mr. Marth for the following notes referring to
Hansen's Calculations of old Solar Eclipses.
The Talue of the acceleration of mean longitude employed in Hansen's
Lunar Tables is i2''-i8o. His further researches (vide Darlegung der
theoretischen Berechnung^ &c., znd part, page 374) have led him to in-
crease this value by o"*377y and he has found, by extending his researches,
corrections of the tabular retardation of the perigee and of the acceleration of
the node.
Hansen's
Lunar Tables. Final Yalaes.
Diir.
Secular Variation of Mean Longitude
„ Perigee
,, Node
+ 12-1 80^
-37255^
+ 7068 /«
+ 12-557^
-38-577'*
+ 6*623 ^
+ 0-377
— 1-322
-0-445
The tracks of the old total Solar Eclipses (arranged in chronological
order) are altered by these corrections in the following manner : —
1. Eclipse of Thales,— 584 May 28.
The zone of totality is thrown 1° 7' towards the north, and covers the
greater part of the whole region within which it may be fairly as-
sumed that the battle between the Lydians and Medes must have
taken place. It covers, also, the Hellespont, and satisfies the remark
of Theon (in his commentary on Ptolemy's Almagest) y who speaks of
an eclipse which was total in the Hellespont and its neighbour,
hood, while at Alexandria the greatest phase was at most |ths of the
Sun's diameter. The northern limit of the zone of totality approaches
also to Boghaskoei, lat. 40^ 2' N., long. 34° 21' E., in the neighbour-
hood of which monuments cut in the rocks have been found, ap-
pearing to refer to the war between the Lydians lind Medes, to the
solar eclipse, and to the succeeding events.
2. Eclipse of Lari88a,>-556 May 19.
The central track given by the tables passes i' north of Larissa. Han-
sen's final values throw the track 8' more north, and the eclipse re-
mains total.
3. Eclipse of Ennius, mentioned by Cicero, — 399 June 21.
The tables make the eclipse total for Rome, 5"* before sunset. Hansen's
corrections give the greatest phase 0*987 (Sun's diameter =1) 12"*
before sunset, which seems quite compatible with the record : ** Anno
ccc quinquagesimo fere post Romam conditam Nonis Juniis soli
luna obstitit et nox." {Cic, De Republica, L 16.)
4. Eclipse of Agathodes,— 309 August 14.
The south-east point of Sicily, Cape Passaro,is about 45' distant from the
northern limit of the zone of totality as given by the tables. Hansen's
corrections increase the distance to about 51'. In the uncertainty of
Agathocles' real position at the time of the eclipse, we are left to con-
jecture how near he may have been to the zone of totality.
5. Eclipse of Stiklastad, 1030 August 31.
The shortest distance of Stiklastad from the central track, as given by
the tables, is 1° 20', and from the northern limit of the zone of totality
1° 9' (or, in case the ellipticity of the Earth is assumed to be ^ instead
of ^t about 2' less). Hansen's corrections reduce these distances to
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Appendix. 187
i^ 1 1' and 59', and increase the greatest phase at Stiklastad from
0*985 to 0*988.
The corrected tabular values represent also— .
6. The Eclipse of Rome, 1567, April 9, giving i"'i as the greatest breadth
of the uncovered part of the Sun, as seen from the Collegium Roma-
num. Keppler's record — ** Clavius in commentario in Sacroboscum
recenset, anno 1567, Apr. 9, Romse Solem non totum defecisse, sed
relictum fuisse ezilem quendam circulum lucentem circumcirca" —
might indeed suggest an annular eclipse; it was however total in
the neighbourhood of Rome, though oxdy fbr a very short time.
If the retrograde motion of the node is less rapid by i%*' in a century
than that of the Tables, an assumption which would be compatible with Brad-
ley's observations, it would satisfy the circumstances of some of the old
edipses perhaps still better. The track of the eclipse of Thales would
go still farther north; the eclipse of Larissa would remain total, though
Larissa would now be near the northern limit; the eclipse of Ennius
would have a greatest phase of 0*979, 11 minutes before sunset; the track
of the eclipse of Agathocles would be thrown farther north, so that the
northern limit of the zone of totality would pass at a distance of 28' from
Cape Passaro. Stiklastad would approach within 40' to the northern limit
of totality.
On the other hand, a diminution of Hansen's tabular acceleration of
mean longitude by h" would not satisfy any of the old records (supposing
that the years are correct). Accepting his final values of the secular varia-
tions of the perigee and node, the track of the eclipse of — 5S4 (Thales)
would be thrown more than 9^ southwards, and would not reach the regions
of th« battle before sunset; the greatest phase of the eclipse of — 556 would
not exceed } of the Sun's diameter at Larissa, and that at sunset ; the
eclipse of Ennius would not be at all visible at Rome, as it would happen
after sunset ; the southern boundary of totality of the eclipse of ~ 309 (Aga-
thocles) would be thrown to about 40' north of Syracuse; the track of the
eclipse of Stiklastad would be thrown i** 18' more south.
Appendix D.
At my request Professor Hansen has been so good as to communicate
to me the following explanation of his reasons for using the larger coefficient
of the lunar acceleration in his Lunar Tables : —
** I have never disputed the correctness of the Theory of the Secular Equa-
tion of the Moon's Longitude, such as Mr. Adams was the first to propound ;
but I am not satisfied with the development of the divisors into series, of
which he has made use, as several other geometers have also done. As
the coefficient which results from Mr. Adams' theory does not accord vdth ob-
servations, it could not be employed for the Lunar Tables : for in the con-
struction of tables, either planetary or lunar, the first condition to be fulfilled,
is to construct them in such manner that they represent observations as closely
as possible, for without this they would be of no practical value, and there-
fore useless.
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1 88 Appendix.
'* Mr. Adams' theory came too late to permit of my making use of it in
my works ; and it was well that it so happened, for I had already fomid by my
own theory a coefficient which represents ancient observations as closely as
could be desired; which is not the case with Mr. Adams' coefficient.
*' As my two Memoirs, entitled Darleyung^ &c. were destined to the de-
Telopment of the calculations by which I had arrived at the coefficients used
in my Lunar Tables, I could not therein employ the theory of Mr. Adams ;
and in the introduction to the Second Memoir, p. 4, I have explained myseki
on this point, adding that ulterior researches on this subject were to be re-
served for a special memoir. Subsequently I endeavoured to account for
the fact that Mr. Adams' coefficient did not accord with observation, and
I found that an extremely small retardation in the rotation of the Earth on
its axis sufficed to explain it ; this was published in the Berichte der K,
Sachs. Gesellsekqft zu Leipzig for 1863, in the note to which you have drawn
attention. Already M. Mayer, of Heilbronn, in his Beitrage sur Dyfuunik
dea HimmelSt etc., a work with which at the time I was unacquainted, had
directed the attention of geometers to the Tidal Wave as capable of causing
such a retardation of the Earth's rotation ; and recently M. Ddaunay has
submitted this point to analysis.
** In the actual position of the question it may be concluded from all these
researches, that the acceleration of the Moon's motion depends on two causes,
that is to say, the decrease of the excentricity of the terrestrial orbit and a
retardation of the rotation of the Earth on its axis, and that it is the com-
bined effect of these two causes which produces the amount of acoeleratioii
which observations show.
'^ It is, however, very remarkable, that under all these circumstances, the
hypothesis that H ss o, in regard to the acceleration, leads to a value for the
coefficient in question which represents the old eclipses as well as can be de-
sired, and which for this reason ought to be considered as the true value of
the coefficient for the secular equation of the mean longitude of the Moon.
" Ootha, 1866, Feb, 10."
" P. A. Hansen.
Appendix E.
Mr. Bosanquet deserves great credit for the zeal he has evinced in pro-
moting the investigation of certain ancient eclipses. It appears that he was
the first to call the attention of Astronomers, and more particularly that of
Mr. Airy, to historical facts in connexion with the expedition of Agathocles,
which it was necessary to take into account in interpreting that eclipse.
Moreover, Mr. Bosanquet urged upon Mr. Airy's attention facts which
induced him to search out and identify the important eclipse of Larissa ; and
he has brought forward evidence tending to show that the appearance oc-
curring to Hezekiah^ is connected with the solar eclipse which took place
— 688, Jan 11, when, he argues, that central conjunction took place about
20 minutes before noon, and that the eclipse was to the extent of about
two-thirds of the Sun's diameter.
* *'And Isaiah the prophet cried unto the Lord, and he brought the
shadow ten degrees backward, by which it had gone down in the dial of
Ahaz." — 2 Kings, xx. 11.
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Appendix. 1 89
Prof. HanBteen was the first to bring under notice the eclipse of Stiklastad,
'' whichy" says the Astronomer Royal, " in combination with that of Larissa,
appears likely to throw light upon the correctness of the lunar tables."
The interest of Mr. Airy in these ancient eclipses is naturally concentrated
upon the data they afford for determining elements connected with the
lunar motions. A perusal of his investigations published in the PhilosO'
phical Transactions in 1853, and in the Memoirs qf the Royal Astronomical
Society in 1858, will repay aU who take an interest in the history of the
development of tiie lunar theory. Although the main object of the papers is
the fixing of the time and place of the phenomena under discussion, with a
view to the correction of lunar elements, yet certain matters of historical and
geographical interest are not neglected. Among these may be cited the
fixing of certain limits within which the battle occurred between the Lydians
and Medes in Asia Minor —s^At ^^7 ^^ l ^'^^ ^^ ^^ landing-place of
Agathodes on the African shore ; lastly, the correction of the longitude
of Nimrud, as given in Capt. F. Jones' map.
Appendix F.
Suppose that Hansen's value is practically required, and that the differ-
ence between the theoretical and the practical value is caused entirely by the
retardation of the Earth's rotation, Hansen, in the remarks already quoted,
tacitly assumes, that, because the time of rotation becomes variable, therefore
the length of the mean day, which is the unit of time of the tables, becomes
also variable. Now, this is not at all such a matter of course. If astronomers
agree to retain as the unit of time a mean day of uniform length, the whole
effect of the retardation of rotation is thrown upon the tables for converting
sidereal time into mean time, and the tables of the Moon and planets remain
perfectly unaffected by the variability of the rotation, and the Lunar Tables
must therefore contain the strictly theoretical value of the acceleration : — this
course of taking account of the retardation seems to be more simple than
the other.
Before retiring from the high and honourable position to
which, for two successive years, you have been pleased to call
me, and resigning into the able hands of my successor the
responsible duties of the Presidency, I desire emphatically to
assure you how fully I have always appreciated the generous
support on all occasions accorded me by my Colleagues in the
G
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190 The Presidents Address,
Council, and by yourselves in this Room. I have never occu-
pied this chair without feeling that I was in the presence of
considerate friends cordially sympathising and coroperating
with me in my continual, however imperfect, endeavours to
make our meetings both instructive and agreeable, and ever
ready to condone, with their indulgent kindness, my inevitable
shortcomings. To each and to all I tender my grateful thanks.
During my tenure of office one or two innovations have
been introduced, to which I now refer simply for the purpose
of stating that they were purely personal, and in no way
binding on any future occupant of the President's chair. One
of these is, the report of the viva voce discussions at our
meetings ; the other is, the annual Reunion of our own Mem-
bers and the members of other scientific bodies, as well as of
other gentlemen of eminent position in political or social life.
It was a matter of great gratification to me to meet so many
distinguished friends and cultivators of science ; and I believe
that such assemblages are productive of good ; but at the
same time I wish it to be understood that I had no desire to
establish a precedent.
And now, let me add that my two years of office have been
to me a source of the highest and purest pleasure.
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Election of Officers and Council. 1 9 1
The Meeting then proceeded to the election of the Officers
and Council for the ensuing year, when the following Fellows
were elected: —
President :
Rev. Chables Pbitchard, M.A. F.R.S.
Vice-Presidents :
Rev. Professor Challis, M.A. F.R.S.
Wabben De La Rub, Esq. F.R.S.
John Russell Hind, Esq., F.R.S., Superintendent
of the Nautical Almanac,
Rev. Robert Main, M.A. F.R.S. Radcliffe Observer.
Treastirer :
Samuel Ghables Whitbread, Esq., F.R.S.
Secretaries :
Richard Hodgson, Esq.
Edward J. Stone, Esq. M.A.
Foreign Secretary/:
Admiral R. H. Manners.
Council :
Professor Adams, M.A. F.R.S.
G. B. AiBT, Esq. M.A. F.R.S. Astronomer Royal.
R. C. Cabbington, Esq. F.R.S.
Professor Cayley, M.A. F.R.S.
Thomas Cooke, Esq.
James Glaisheb, Esq. F.R.S.
Rev. Fbbderick Howlett.
William Huggins, Esq. F.R.S.
John Lee, Esq. LL.D. F.R.S.
Captain William Noble.
J. Norman Lookyeb, Esq.
Major-Gen. Shortbede.
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192
CONTENTS.
Page
Fellows elected .. 93
Report of the Council . . . . . . 94
List of Papers read from February 1865 to 1866 . . 152
List of Donors to the Library . . • • '55
President's Address on delivery of the Gold MedfU to Prof. Adams . . 157
Election of Officers and Council 191
Printed bySTRANGSWAYS and Walden, Castle St. Leicester Sq. and Published
at the Apartments of the Society, March 7, i860.
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MONTHLY NOTICES
OF THE
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVL March 9, 1866. No. 5.
Rev. Charles Pritchard, President, in the Chair.
John Matheson, Esq., Glasgow ;
Jabez Moden, Esq., Wellington Street, Gloucester ;
Rev. D. W. Durnell, Welton, Northamptonshire ; and
Dr. Dodgson, Cockermouth,
were balloted for and duly elected Fellows of the Society.
InvestigHtions on Airifs Double-Image Micrometer,
By Prof. F. Kaiser, Director of the Observatory at Ley den.
Tlie director of the RadclifFe Observatory, Oxford — the
Rev. R. Main — has desired that 1 should present to the Royal
Astronomical Society a brief account of my investigations of
Airy's Double-Image Micrometer, and I feel honoured in satis-
fying that desire. These investigations form however only a
small part of my investigations on micrometer measurements in
general, which I can still by no means consider as closed, and
the complete description of which would require a whole
volume. Therefore I must limit myself to mentioning a few
results, that may be of some value for those who possess and
use Airy's Double- Image Micrometer, and I hope at least to
Digiti
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194 -P^^' Kaiser y Investigations on
give hereby a proof of the high value which I attach to this
important English invention. '
Already in the year 1855 Mr. W. Simms made, at my
request, a double-image micrometer of Airy's invention, with
a position -circle, for the Observatory at Leyden. This in-
strument was destined to be added to my 6-inch refractor
there, and to serve for the measurement of planets, 'for which
the wire-micrometer appeared less appropriate. Though Mr.
Simms has delivered the instrument for the moderate price
of 16/. 165. it is very beautifully executed, and the modi-
fication of its construction that appears to me desirable would
not be possible without considerably increasing its price.
The Astronomer Royal himself has given, in the Green^
wich Observations^ in the Memoirs of the Royal Astronomical
Society, vol. xv., and in the Monthly Notices of the Royal
Astronomical Society y vol. x., a complete theory and descrip-
tion of his double-image micrometer, therefore I may consider
the instrument as suflficiently known. From that theory and
description it appears that, with the double-image microme-
ter, errors are to be feared arising from the following sources :
— (i.) Periodical errors of the micrometer screw ; (2.) Vari-
ability in the mutual distance of the threads of that screw ;
(3.) Distortion of the images. The periodical errors of the
screw may be very different at small differences in the read-
ings of the micrometer-head, and require therefore a particu-
lar inquiry. The errors arising from the sources (2) and (3)
do not compensate themselves in brief periods, and their com-
mon amount may be determined by the same inquiry.
In the micrometer of Simms one half-lens is quite fixed,
while only the other can be moved by the micrometer-screw.
This construction makes it impossible to eliminate the periodi-
cal errors of the screw at the measurements themselves. If the
fixed half- lens could only be moved so much as the amount of
one revolution of the micrometer-screw, we could hereby, ac-
cording to Bessel's theory, eliminate at each measurement the
periodical errors of the screw, and this would be a great gain.
If the fixed half-lens could be moved as much as the moveable
one, the measurements could be extended to angles twice as
large as can now be measured with the micrometer. Then it
would however be necessary that the two half-lenses should
be shown together, with relation to the fixed lenses. By this
modification the price of the instrument would certainly be
considerably raised, but it would be worth while.
I should require too great a space to describe here in what
manner I have determined the periodical errors of the screw
of Airy's micrometer, while the instrument is not adapted to
this inquiry. Therefore I will only mention the results ob-
tained, from which it appears that the periodical errors of
the screw are very considerable, and very different in its
different parts. The scale by which the revolutions of the
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Airy* 8 Double-Image Micrometer, 195
screw are counted is extended from o to 50. In the year 1863
I demonstrated, bj many hundreds of measurements, the peri-
odical errors of the screw, from 5 to 5 revolutions, between
the readings of the scale 10 and 40. If the periodical error be
expressed, as usual, by the periodical function :
^ («) >■ a cos » + 6 sin u + c cos 2 « + <? sin 2 tt +
in which u signifies the reading of the micrometer-head, trans-
formed into degrees, according to my inquiry, we have for the
periodical errors of the screw in its different parts, the fol-
lowing values: —
Scale
10 (p{u) = — 1*075 COS u — 0*578 shi ti — 0*149 COS 2M — o'022 sln 2 u
J5
— o*8o6
- 0*934
-0*183
— 0*025
20
— 0*720
- o*975
- 0'2l6
+ 0*046
25
~ 0*721
- 1*283
— 0-146
+ 0*051
30
-0-655
- 1-338
— 0*142
+ o*o68
35
-0*835
- '-5^7
— 0*140
+ 0*135
40
- 0729
— i'7ii
— 0*310
+ 0-195
It appears, therefore, that the errors of the screw are very
variable, and, in themselves, five times larger than those of
Bessel's heliometer.* The value of one revolution is, how-
ever, for the heliometer 5 2" and for Airy's micrometer, accord-
ing to the different powers, from 5" to 1 1", so that the influence
of these errors is from 5 to 10 times smaller than with the
heliometer. The errors are however far too great to be neg-
lected.
The common amount of the errors (2) and (3) is obtained by
determining the value of the revolution of the screw for differ-
ent values of the measured angle, or, which is the same thing,
for different distances of the half-lenses. This amount will be
imperceptible if, for all the distances of the half-lenses, there is
found the same value of the revolutions of the screw, and then
the movement of the half-lens will be sensibly proportional to
the size of the objects that are to be measured. It is however
extremely difficult to determine, with the required accuracy,
the value of the revolutions of the screw. Even though Bessel
had not positively declared it,*|" we could easily be convinced,
by our own experience, that no observation of transits, or
angle-measurement with a circular measuring instrument, can
* Bessel, Asironomische Untersuchungeny vol. i. p. 83.
t Bessel, Asironomische Nachrickteriy No. 403, and Astron, Untersuchun-
geny vol. i. pp. 51 and 132.
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196 Prof. Kaiser^ Investigations on
give a micrometrical accuracy. Bessel preferred a heliometer,
even for measuring small angles, because with that instrument
it is possible to embrace also angles of more than one degree.
If the value of the revolutions of the screw were determined
by the ordinary means for a space of more than one degree,
the inevitable error committed in this would be considerably
diminished in angles of a few minutes, which are peculiarly
to be measured by the instrument. With Airy's micrometer
it is hardly possible to exceed the small angles that are to be
measured therewith, and the errors committed in determining
the revolutions of the screw are therefore not diminished in
the results of the measurements which are to be performed with
the instrument. I had requested therefore that Airy's micro-
meter, that is, a terrestrial eye-piece, should be constructed in
such a manner that it might ,be directed on the wires of the
wire-micrometer. The distance of the wires can be determined
with the wire-micrometer free from all errors of the instru-
ment. If that distance be measured again with Airy's micro-
meter, we might, with a micrometrical accuracy, derive there-
from the value of the revolutions of the screw, and Airy's
micrometer would give the same accuracy as the wire-micro-
meter, in those cases in which the latter instrument, on ac-
count of the diffraction of light, does not allow a sharp defini-
tion. Unfortunately Airy's micrometer could only be adapted
to the wire-micrometer with its two lowest powers, which are
too small to allow any sharp measurements.
Airy's micrometer has four first lenses, with focal distances
of h h h ^^^ ' inch, which give, with the 6-inch refractor,
magnifying powers of 326, 220, 143, and 109 times. Already
in the year 1856 the value of the revolutions of the screw was
determined for each of those powers, and for very different
values of the measured angle. For doing this, with the two
highest powers, the wire-micrometer was screwed on a refrac-
tor of Steinheil having an aperture of 4 inches and a focal
distance of 9 feet, while Airy's micrometer was adapted to
the 6-inch refractor. The object-glasses of both the refractors
were directed on each other, and with Airy's micrometer the
image of the wires of the wire-micrometer formed by both the
object-glasses was measured. For the two lowest powers the
micrometer of Airy was immediately adapted to the wire-
micrometer. Thus the value of the revolutions of the screw
was determined, with great care, for the different powers and
for different measured angles, and I gave an extensive report
of these investigations, with a number of remarks on Airy's
micrometer, in an ample treatise that was, in the year 1857,
published by the Royal Academy of Sciences at Amsterdam.*
After the foundation of the new Observatory at Leyden, in
* The title of that treatise, Eerste onderzookingen met den Mikrometer
van Airi/t volbragt door F. Kaiser. Amsterdam : C. G. van der Post.
1857.
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Airifs Double- Imfige Micrometer, 197
the year 1861, the 6-mch refractor was exclusively destined to
extra-meridional observations of planets and comets, and the
new 7 -inch refractor of Merz was destined to micrometer
measurements. Airy's micrometer was adapted to the 7-inch
refractor, and, in the year 1 863, 1 undertook a new investigation
of Airy's micrometer, in quite a different manner from the for-
mer, in order not to be obliged to dismount the instrument for
it. To the edifice of the University, at a distance of 240
metres from the refractor, I fixed a heavy black shelf, to
which were attached some silvered copper disks. Two of these
disks were very small, and were placed at a mutual distance of
about 0*50 metres. The remaining disks had diameters of about
O'oi, 0'02, 0*03, 0*04, 0*05, and o'o6 metres. The linear dimen-
sions of these diameters, and of the distances of the small disks,
were accurately measured, and this made known the ratio be-
tween these quantities. The anguUr value of the distance of the
small disks was afterwards determined by the wire-micrometer,
and, by the said ratio, from this, by proportion, the angular
value of the diameters of the larger disks was derived. The
angular distance of the smaller disks, amounting to above 7',
could Jbe determined with a certitude of about o"'i ; and, as
the diameters of the disks were from 8 to 50 times smaller,
the angular values of these diameters became known with a
certitude of o"oi or o"-02. The diameters of the disks were
measured again with Airy's micrometer, and so the values
of the revolutions of the , screw were determined for different
distances of the half-lenses. When however I had measured
two of these disks, with all the powers of the micrometer eye-
piece, and each of them 50 times, my shelf with disks disap-
peared, without my being able to discover who had taken it
away, and my investigation was broken off.
In the past year I had new disks made that were fixed to a
piece of iron, and were attached to a part of the edifice of the
University, where they- were more safe than before. The
measurements were repeated in the former manner, and ex-
tended with Airy's micrometer, on five disks, with diameters
of 8" to 45". The result for each disk and each power
rested on no less than a hundred pointings and readings. The
silvered disks however soon gathered moisture, and they
were soon so little brighter than the blackened iron that the
measurements were extremely difficult.
Lately I effected quite a new investigation with respect to
Airy's micrometer, in which I superseded the former disks by
artificial double-stars. To the above-mentioned iron were
screwed copper-plates with little apertures that appeared, by
the refractor, under an angle of o"*8, and at such distances as
that they represented double-stars at distances of 7''* 5 to 74"* 6.
Behind the iron was placed a mirror that reflects the daylight
through the apertures towards the refractor, and by which
these apertures show themselves very clearly with a clouded
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198 PTof. Katsevy Investigations on
sky. After these artificial double-stars were measured lineally,
with great care, I measured each of these objects 50 times witl.
the second power of Airy's micrometer.
All the above-mentioned inquiries have, without an excep-
tion, led to the result that the value of the revolution of the
screw of Airy's micrometer increases with the measured angle,
and that therefore the movement of the half-lens is not pro-
portional to the distances of the images, and that a consider-
able error may be committed by assuming a constant value for
the revolution of the screw. I cannot communicate my thou-
sands of measurements for the investigation concerning Airy's
micrometer with any completeness without requiring a space
that I cannot dispose of here, but, as a proof, I communicate
the measurements performed with Airy's micrometer, in the last
year, with the second power, on eight artificial double-stars.
Each of these objects which I shall name a, b, c, rf, c, f, g^
and hy was each day measured five times, and these measure-
ments were repeated on ten different days, so that each re-
sult rests on a hundred readings. The results obtained each
day, and expressed in revolutions of the screw, are the follow-
ing \—
a
h
c
d
e
/
9
h
0-9862
2-0133
3-0023
3'9995
5-2918
6*2845
7-1445
9.7666
0-9924
2-0084
»-9943
3-9805
5-3083
6*2898
7*2382
9-7657
10019
2*0009
3-0067
3.9909
5-3026
6-2957
7-2611
9-7792
0-9954
2-0055
3-0002
3-9858
5-2856
6-2948
7*1448
9-7658
0-9891
1-9967
3-0148
4-0083
5-3001
6*2988
7-2673
9-7667
0-9975
1-9993
3*0072
3-9887
5-3188
6-2889
V^l^S
9-7715
0-9977
2-0065
3-0065
3.9932
5-3011
6*2944
7*2709
9-7810
1-0041
2-0088
3-0192
4-0098
5-2993
6*3089
7*2810
9.7907
1-0068
2*0131
3-0113
4-0044
5-3698
6-2974
7-2626
9*7015
1-0149
2-0281
3-0207
4-0048
5-3248
6*2978
7*2630
7-2608
9-7873
1 0-9986
2 -008 1
3-0083
3-9966
5*3042
6-2951
9*7756
Airy's micrometer gives, with the 7 -inch refractor, powers
of 413, 278, 178, and 137 times. For the above-mentioned
measurements the second power, namely that of 278, was used.
If it be remarked that, with that power, the value of a revo-
lution of the screw amounts to about 7"*5, it immediately ap-
pears from the above measurements that Airy's micrometer
admits of a great accuracy, and therefore deserves a rigorous
investigation. The above results require however still a small
correction that arises from the manner in which I performed
the measurements. If we call the images formed by the one
half-lens m and w, and those formed by the other m' and n', n
Digiti
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Airt/^s Douhh' Image Micrometer. 199
and m! were brought, as nearly as possible, under each other,
and placed so that the line passing through their centres stood
perpendicularly to the line that connects m and n' together.
This was done by the moveable half-lens on the left-hand ;
by the moveable half-lens on the right-hand the same thing
was done for m and n!. Of course the micrometer-screw was
always turned in the same direction. Half the difference of
the readings would have been precisely the distance of the
centres if the images fell into the same straight line, but now it
is a little too small. I chose this manner of measuring because
it appeared to me it allowed a very sharp definition, and ex-
cluded the possibility of constant error. After applying the
necessary small corrections, I found, for the true distances in
revolutions of the screw, the following final results : —
a b c d e f g h
1*0043 1*0109 3*oioi 3*9980 5*3053 9*2959 7*2616 9*7762
With a comparator that I had composed from parts of other
instruments, I repeatedly measured the linear distances of the
different artificial double stars, and I got for this the following
results, expressed in millimeters : —
a b c d e f y h
8625 17*455 26*253 34'9'5 46*365 55'i95 63*820 86*290
The distance of the two most distant small apertures was
480 038 millimeters, and by often repeated measurements with
' the wire-micrometer in which the periodical errors of the screw
were eliminated, it was found that this distance amounted to
20*02 1 3 revolutions of the screw of the wire-micrometer. The
value of each revolution of that screw had, by very numerous
passages of stars, while the wires were 13' distant from each
other, been determined to be 2o''"j 1 5, and from this ensued, by
proportion, for the distances of the artificial double-stars, in
seconds : —
a b c d e f g h
7*452 15*080 22*681 30M65 40*057 47*686 55*138 74*550
From these numbers we find, with the second power of
the micrometer, the following results for the value of each re-
volution of the screw. The number above each result signifies
the distance of the half-lenses, expressed in revolutions of the
screw, corresponding to the revolution which has been
found : —
Digiti
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200 PTof, Kaiser, Investigations on
a
b
e
d
e
/
9
;i
I^x)
roi
301
400
5-31
6'30
7-a6
978
tf
*
n
#
', ,
'^^o
7'499
7*535
7*545
7-550
TSIA-
7'593
7'626
From this it appears therefore, that the value of the revo-
lutions of the screw increases very sensibly with the size of
the measured angle, and all the investigations of the same na-
ture, performed with the micrometer, have led to the same
result.
Constant errors in the measurements might cause different
results to be found for the value of the revolutions of the screw
at different angles, even if the micrometer were perfect. Thus,
for instance, assuming that a and A have both been measured
3*01 revolutions, or o"*23 too large, the same result, namely,
7"-649, would be found, but in the actual measurements it was
totally impossible to commit a constant error of that amount.
The measurements on the remaining artificial double stars are
also contrary to the supposition of a constant error. If, namely,
we assume'the value of 7"*649 for all the artificial double stars,
the errors of the measurements should have the following
amounts : —
— 0*23 —0*30 — o*34 —©•4a —0*52 — o*47 —0*41 — 0*23
As well the amount as the regular increase and diminu-
tion of these differences renders the supposition absurd that the
value of the revolutions of the screw was constant. Although
I was convinced that the errors of the above results could at
the utmost amount to a few hundredth parts of a second, I have
measured four of the artificial double stars — namely, a, h^Cf
and d — once more in a quite different manner. If we again
name m and n the two objects of the one image, rn! and n
those of the other ; I now brought all the objects into the same
straight line and placed, with movable half-lens on the left
hand, the object m! first on the left and then on the right of
«, so that there remained each time a black space as a mini-
mum visibile. Afterwards the same was done by movable half-
lens on the right hand with the objects m and n, and the dis-
tance of the centres was thus obtained by four measurements
instead of by two. I repeated the measurement each day five
times, and performed this on eight different days. The results
obtained on those days are the following : —
a
b
c
d
I -0060
2*0165
3-0199
4*0042
1*0030
2*0132
3*0147
4*oo8i
0-9959
2*0181
3*02I2
4-0045
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Avtifs Double-Image Micrometer. 201
a
h
c
d
o'9979
1-0095
3*0175
4*0077
1-0057
2*0156
3*0179
4-0007
1-0034
2-CI53
3*0156
4-0070
0*9961
2*oio6
3-0183
4-0045
I -0062
2-0134
3*0153
4-0066
Mean I'ooiS
2*0140
3*0175
4-0054
The absolute differences compared with the former results
are for —
a h c d
M M K
+ 0-02 — 0*02 — 0*05 — 0*05
Although the differences are greater than I expected,
they are small enough to exclude the possibility of errors that
amount to o"*52. I prefer the first method of measuring, as it
appears to me to allow the greatest accuracy in pointing.
If the value of a revolution of the screw is assumed to un-
dergo a change proportional to the size of the measured angle ;
if X is named the value of a revolution of the screw for a dis-
tance equal to zero, and y the increment of that value for each
revolution of the screw, each of the artificial double-stars gives
an equation of the form —
m — nx ■><■ if^y.
The solution of the eight equations obtained in this man-
ner, according to the method of least squares, gave —
w = 7*4791
y s= + 0*01511
and therefore, if r signifies the value of each revolution of the
screw, and R the dimension of the measured angle in revolu-
tions of the screw —
r = 7*479X + 0*01511 R.
If we calculate by this the value of r for the different arti-
ficial double-stars, we get for —
Digiti
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Prof, Kaisevy Investigations on
Observed
7-420
7*499
7*535
7*545
Calculated
7*494
7-509
7*5*5
7*539
Difference
+ 0-074
+ 0-0I0
— O'OIO
— 0-006
Absolute error
— 0*07
—0-03
+ 0*03
+ 0-02
e
/
9
h
Observed
7-550
7*574
TS9\
7-626
Calculated
7*559
7*574
TS^
7-624
Difference
+ 0*009
o-ooo
—0-004
— 0-002
Absolute error
— 0*05
0-00
+ 0-03
+ 0*02
The amount of the absolute error at a seems to indicate
that the value of r increases more slowly in proportion as R
grows larger. This deserves attention, since the second series
of measurements also agrees with it.
In order not to make this paper too extensive, I will only
mention, as regards my remaining investigations on Airy's mi-
crometer, the final results of the measurements on five metallic
disks performed in the year 1865. By very numerous measure-
ments the diameters of these disks were found thus : —
I
2
3
4
5
In Millimeters
9-987
20-020
30-047
40-027
45 928
In Seconds
8-628
17-296
25-959
34^581
43'''i35
The diameters of these disks were, with the powers i, 2,
and 3 of Airy's micrometer, measured on each day five times,
and these measurements were repeated on ten different days.
The final results, expressed in revolutions of the screw, are
the following : —
I
2
3
4
5
Powpr I
1-7407
3-4496
5-1267
6-8082
8-4488
Power 2
I-I535
2-3124
3*4531
4-5898
5-7117
Power 3
0-7596
1-4983
2-2341
2-9703
36930
From this follows for the value of r : —
I
2
3
4
5
Power I
4*957
5-014
5-063
5-079
5*105
Power 2
7-480
7-480
7-518
7*534
7*55^
Power 3
11-359
"'544
11-620
11*642
11-680
Consistently with all the investigations performed, we
tized by Google
Digitiz
Avnfs Double- Image Micrometer, 203
see here again r increasing when the measured angle grows
larger.
If we assume for the second power the before-found value
of r, r = 7"'479i -|- o"'oi 511 R, we have for r at the different
disks of which the diameters have been measured —
I
2
3
4
5
Observed
7-480
7-480
7-518
7'534
7*55*
Calculated
7-496
7*5H
7-531
7-548
7-565
Difference
+ o-oi6
+ 0034
+ 0-013
+ 0-014
+ 0-013
Absolute Error —0*02 -o*o8 —0*04 — o-o6 —0*07
It appears therefore that the disks have been measured
rather too large, which cannot be astonishing, since by the in-
terference of light they must show themselves rather larger
than they are. The result that Airy and Liouville have ob-
tained by measurement, that the apparent diameters of disks
are, contrary to theory, independent of the apertures of the
refractors, deserves indeed a further inquiry. The mean of the
absolute errors is — o"'o^6. If we assume this amount, the
remaining errors are, with
— 0-04 +002 — O'OI +0-0I +0'02
The measurements on the disks were sensibly less sure
than those on the artificial double-stars, because the former
very soon lost their whiteness. The disk i especially was
generally very faint. I intend to repeat this inquiry with
round apertures through which the daylight shines. It will
hardly be necessary to remark that all the measurements re-
corded here are freed from the periodical errors of the screw.
It is easy, by a repetition of observations, to give to a final
result of micrometer-measurement, a probable error of only a few
hundredth parts of a second, but that probable error is a false
measure for judging of the real error. It is ordinarily seen
that final results for the same dimension, obtained by microme-
ter-measurements, differ some tenth-parts of a second from one
another ; and if it is considered from what complicated opera-
tions the above results have been derived, we have reason to
be very well satisfied with their mutual harmony. An object
with a diameter of one second presents itself, even with a
power of 300, still so small to the eye, and the air is, more-
over, continually so impure and unquiet, that we must despair
of performing micrometer-measurements with a certainty of a
few hundredth parts of a second, and I do not believe that this
accuracy has ever been obtained, however small the probable
error of the final result may be.
Digiti
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204 M. Hoeky Additons to the
From the above-mentioned investigations it appears that
the Astronomer Royal has, by the invention of his double-
image micrometer, rendered an important service to Astronomy.
I doubt very much whether, besides the Heliometer, a second
double-image micrometer exists by which measurements can
be effected so accurately as by Airy's double-image micrometer.
That instrument requires however a very rigorous and diffi-
cult inquiry in order to give it the accuracy of which it is ca-
pable, and it requires also great prudence in the use of it. In
my treatise of the year 1857 I have treated circumstantially
of the precautions that Airy's micrometer requires, and of its
properties.
A micrometer like Airy's can only render its services if it
is adapted to a large and precious refractor. The price of the
micrometer would, even if it were doubled, still remain very
insignificant in comparison with that of the refractor. There-
fore I should think it very desirable to give to the micrometer
the above-mentioned more complicated construction, even if
its price were thereby considerably increased. It would be
very important if the periodical errors of the screw could be
eliminated by the observations themselves, and, by a mobility
of the fixed half-lens, the measurements could be extended to
angles twice as large as those which the micrometer is now
capable of measuring.
Lej/deUf Feb, 1866.
Additions to the Investigations on Cometary Systems,
By M. Hoek.
In § 1 1 of my paper " On the Comets of 1677 and 1683,
i860 III., 1863 I., and 1863 VI." present volume, pp. 1-12,
I announced the necessity of a new combination of our whole
stock of cometary aphelia with adequate enlargement of the
limit of time. I have effected this investigation.
In order to have before the eye the whole of the pheno-
mena furnished by the distribution of cometary aphelia and
planes of orbits, I have made a drawing containing 1 90 orbits
of comets discovered since the year 1 5 56.* First, I laid down
in it the aphelia whose positions were obtained by calculation
after the elements that seemed to be the most reliable.
Further I traced through these aphelia the circles which re-
* Periodical comets and elliptical as well as uncertain orbits have been
excluded.
Digiti
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Investk/ations on Cometary Systems. 205
present in a stereographic drawing the intersections of the
planes of the orbits with the sphere. But, in order to avoid
a confusion which would have been intolerable, I limited these
circles to a length of 10° in average on both sides of the
aphelion.
It was the intention to find out those points of the sphere
in which occurred an intersection of several orbits, the aphelia
of which were distributed around these intersectional points.
For, having discovered such points, we have reasons to presume
that they indicate, each of them, a centre of cometarj emana-
tions, such as the point
I A = 3i9® /3-i — 78°*5 Mean Equinox of 1 864*0.
the discussion of which was given in my former papers.
I find that it is possible that there are such centres in the
following positions : —
II X « 2670 jS — — 51*6 '^
ni A - 175-5 /J --46-5
IV X - 75*5 ^ =-51*7
V X = 274-6 /J =+38-7
VI X = 92-9 /J — + 0-6 /
Mean Equinox of 1864*0
and I proceed to indicate what there is remarkable in each of
them.
II. is the intersectional point common to the orbits of the
comets of 1739, 1793 IL, 1810 and 1863 V. Unfortunately
for our purpose, there is uncertainty with respect to one of
these comets. It is possible, and even somewhat probable, that
the Comets of 181 o and 1863 V. are two apparitions of a same
body revolving every 53*3 years.
III. is the centre of a small circle of 1° in diameter, through
which pass the orbits of the Comets of 1764, 1774, 1787, and
1 840 III.
IV. is the centre of a small circle of 1° in diameter, through
which pass the orbits of six comets, those of 1596, 1781 I.,
1790 in., 1825 I., 1843 IL, and 1863 III. At a small dis-
tance from this circle pass the orbits of the Comets of 1785 II.,
1818 II,, and 1845 ^i^- ^"* yf^ySiX gives to its centre a pecu-
liar interest is that it is only i°-5 distant on the sphere from
the p<)int
X ^ 73°-2 ^ =— 5i*-6 Mean Equinox of 1864-0
in which occurs the intersection of the orbits of the Comets
1857 III. and 1857 V. As for me, I do not doubt that
these two comets are members of a former system, when I
Digiti
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2o6 M. Hoehy Additions to the
consider how email the interval of time was between their
apparitions, and how uncommonly great the resemblance is in
all the elements of their orbits.
It is true that among the eleven orbits, which may be con-
nected with the point IV., there are some whose aphelia are
distant from it by more than io°, the average distance I
had adopted. But we must remember, first, that there is
something arbitrary in this limit ; secondly, that we ought not
to consider as exactly known the aphelia such as they are
given by the computation of the orbits. Let us remember
that often it is possible to represent the observations of a
comet in diiferent manners, by varying the longitude of the
perihelion, and according to it the time of its passage. Fur-
ther, that very often, when the comet is still at a great distance
from us, the observations are rendered less certain by the cir-
cumstance that no nucleus is visible. Finally, that generally
when the comet has approached our earth, and when we per-
ceive its nucleus, its movement must necessarily be modified by
the reaction it has to suffer from the particles evaporating
under the influence of the Sun.*
V. is the centre of a circle of 3® in diameter traversed by
the orbits of the Comets of 1773, 1808 I., 1826 II., and
1350 II. Unfortunately the orbit of the second of these is
less certain.
VI. is the centre of a small circle of 52 minutes of angle in
diameter, within which are accumulated the aphelia of the
Comets of 1689, 1698, 1822 IV., and 1850 I.
The probability, a priori^ of this phenomena being
(sin*. 13')' or o, 000 000 000 000 002925,
we could have expected its occurrence by chance only once in
341900 000 000 000 cases, and all our comets (190) furnish
I
only 52590000 quaternary combinations, that i^ i.
part of the required number.
It is very unfortunate, indeed, to have here again a reason
to doubt. The orbit of the Comet 1689 is rather uncertain,
and the allowable variations of the elements would easily
remove the aphelion far from the indicated limit of position.
Let us, however, observe that even when the orbit 1689 is
wholly rejected, the point VI. retains a deal of its interest.
* It appears even probable to me that we must admit such influences in
the aphelia of the Comets 1618 II., 1723, 1798 II., 1811 II., and 1849 l-»
all lying around the point
VII X = 2i7°*8 /3 = + 260*6 Mean Equinox 1864*0;
in which four of these orbits meet, and which is only distant from the fifth
^♦^he orbit of the Comet of 1723) by 2°'i.
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Investigations on Cometary Systems* 207
In order to show this, I have repeated the calculation, admit-
ting that only three aphelia are contained within the circle.
The probability of that phenomenon is (sin* 13')* or
o, 000 000 000 2046, and therefore we may expect to find it
once in 4889 000 000 000 ternary combinations. Now, that
number of cases would only be furnished by more than 3050
comets, that is to say, sixteen times the number which actually
has entered into my calculations.
I believe that it is sufficient to have called the attention of
astronomers to these points of the sphere. Generally, there is
too much doubt about the elements as well as about the
periodicity of ancient comets. I do not wish to give here
any decisive conclusions, and I expect the confirmation of my
views from the future apparitions of such bodies. But, there-
fore, let me repeat it, it is necessary that their discovery be as
much as possible assured.
A single remark finally. My drawing of aphelia shows a
very remarkable phenomenon. Let us draw a circle through
the points of the sphere
o o
X - 95 /5 = o
X = 169 /3 = 32
X « 243 ^ = o
I say that the sector contained between this circle and the
ecliptic is uncommonly poor in aphelia. Indeed, instead of
containing fifteen of them, which would be required by a
uniform distribution, it only contains one, that of the Comet
of 1585, situated at 3° distance from the ecliptic.
How are we to explain this ? If we knew that the solar
system was removing from the point situated in the middle of
that sector, I should be inclined to attribute the phenomenon
to a difficulty Comets might experience in overtaking the Sun.
But the direction of the solar motion, such as it was given by
Madler's investigations, does not allow of such an explanation.
Therefore we may ask if the phenomenon is a real one, and
there is in that direction of the heavens a scarcity of centres of
cometary emanations ; or rather, if it depends on the circum-
stances under which comets are ordinarily detected, the sector
in question being so near the part of the ecliptic occupied by
the Sun from July to December.
Utrechtf December ^f 1865.
M. Hoek has communicated the following corrections to his
former papers : —
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2o8 Rev. T. W. Webb, Notice of the Great Nebula in Orion,
In the first paper, vol. xxv. pp. 243-25 1, § 2, the formula
COB i « — - — ( - + I ) should be cos I = ( - — ' )
In the second paper, present volume, pp. 1-12, § i, note to
the Comets 1672, 1677, and 1683, 1677 is a stranger, should
be 1672 is a stranger.
§ 2, belonging to the cometary systems of 1 860 and 1 863,
should be cometary system.
§ 6, the equations quoted from the Theoria Motus Corpo-
rum Ccelestium, v should be r.
Same §, p. 9, line 21 from the bottom, to be reduced to
-|th part, should be |th part.
Same §, p. 9, line 6 from the bottom, repetition of perihelia,
should be repartition.
Notice of the Great Nebula in Orion. With a Drawing.*
By the Rev. T. W. Webb.
A comparison of the various representations of the Great
Nebula in Orion, which have been given for a period of many
years, seems to lead inevitably to the conclusion that our
knowledge of its real aspect is still far from complete. While
Mr. Huggins' most important discovery of its true constitution
renders the idea of change more conceivable, it must be ad-
mitted that any alterations of form or brightness which may
have been in progress since the employment of the telescope
are so masked by discrepancies of delineation as to preclude
the possibility of drawing any fully satisfactory conclusion.
It would be superfluous to refer to the variations which are so
well known to arise from diversity of weather and instruments,
and eyes and pencils, and especially from the unwarrantable
carelessness of engravers : it only remains to be considered
whether these are the sole causes of the striking differences by
which we are confronted ; or whether, after making due allow-
ance for all these sources of error, there may yet be a residuum
of actual physical change. No other means of investigating
this point seem so promising as the multiplication of designs
by different observers, in different climates, and with different
optical means. From such an accumulation of testimony we
might hope to deduce a much closer approximation to the
truth.
But if I have, from this impression, been led to attempt a
very unpretending sketch, and to beg permission to lay it
before the Society, I trust it will be understood that I am so
sensible of its deficiencies that I should not have ventured to
bring it forward in any other form than that of a suggestion,
* The drawing was exhibited at the Meeting. — Ed.
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Rev. T, W. Webb, Notice of the Great Nebula in Orion. 209
and with the hope that while there are so many instruments,
on all sides, of greater optical power than my own, this refer-
ence to so interesting a subject, may induce some of their
possessors to outdo, as they easily may, all that I have at-
tempted here.
The sketch, of which a copy is now offered, was com-
menced in December 1 863, and continued in a very desultory
manner and with many interruptions till the present season,
when, as the design was carried on into fresh regions, the
detection of one or two features which do not appear distinctly
in previous delineations, determined me to bring it forward at
once, though merely as a temporary and provisional effort, to
be perhaps corrected some future day b/ myself, and certainly
improved by others. Had the weather not been so very un-
propitious, I believe the region N. of the trapezium might
have had a chance of being better represented ; unfortunately,
this is the Yery part to which I should wish especial atfention
to be directed; but I have been unwilling to incur further
delay, as the present season for examination will so shortly be
passing from us.
In this rough attempt to show some part of what may be
visible in a certain circumscribed portion of the nebulosity,
with an achromatic of 51- inches aperture, and' an eye of
average capacity, the object has been to represent the general
arrangement of the luminous haze ; and the iew stars contained
in the sketch are inserted merely for the purpose of more
convenient identification and reference.
The three or four distinct masses of light S. of the tra-
pezium were drawn at the end of 1863 and during the ensuing
spring.
1864, Dec. 27. I suspected the existence of a narrow dark
channel connecting the inner end of the Sinus Gentilii with a
dark opening lying further on in the same direction, which
does not appear in the design of Sir John Herschel, but is
found in that of Bond.
1866, Jan. 5. Though the constellation had not risen more
than half way to the meridian, and definition was fluttering, I
perceived with powers of 1 1 1 and 212a dark rift, of irregular
breadth, lying on the whole nearly in a straight line a little
S. of the stars 87 and 70 (those represented in the sketch).
At the E. end it seemed to communicate with the Sinus
Magnus; at its opposite extremity it opened into a dusky spot
or lake, forming its darkest portion. It appeared broader
S.W. of the star 87 than S.W. of 70. About half-way be-
tween 65 (the P. star of the trapezium) and 87, but a little in
front of the joining line, there is a bright knot, at times
seeming to inclose a minute star.
1 866, Jan. 1 1 . Though near the meridian, I did not see
the dark rift so well as on Jan. 5. I could, however, distinctly
make out the "lake" at its W. extremity. Its N. edge in
Digiti
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2IO Rev, T. W^ Webby Notice of the Great Nebula in Orion.
passing stars 87 and 70 seems a continuation of the Sinus
Magnus, and the rift extends probably right through the
luminous region W. of the lake. I do not think the projecting
end of the Regie Huygeniana to the S. quite so conspicuous,
as compared with the masses lying N.E. and N.W. of it, as
when I sketched it in 1863 and 1864.
1866, January 25. The rift could still be detected, espe-
cially by averted vision, notwithstanding a moon two days past
quadrature. It seems to be feebly traceable beyond the "lake"
to the W. into the dark opening which continues the direction
of the Sinus Gentilii in Bond's drawing, so as to establish an
uninterrupted, though in part very faint, demarcation round
two sides of the brightest portion of the nebula, reaching from
the mouth of the Sinus Gentilii to the bottom of the Sinus
Magnus, With 450 the rift is still pretty distinct; in the
triangle formed by the centre of the new lake, and the stars 6y
and 70, the F. side is longer than the P., and the N. the
shortest of all.
1866, Feb. 3. The sketch was completed for the present.
I have the less hesitation in bringing forward these parti-
culars as I have the pleasure of knowing that my observations
on this rift and the "lake" or opening have been in great
measure confirmed by Mr. Knott with his beautiful 7J-inch
object-glass; and I, therefore, believe there will be little dif-
ficulty on the part of any adequately provided observer in
verifying them. As some indication of the extent of my
instrumental means I may mention that, under suitable circum-
stances, I have never failed to make out the Pons Schroteri
and the nebulosity of the included part of the Sinus Magnus,
since I first caught sight of it a few hours previous to the
great earthquake on the night of Oct. 5, 1863. I have also,
during the present season, repeatedly distinguished traces of
the Nebula Oblongata. The Lacus Lasselii I find, however,
very difficult ; and it is certainly much less conspicuous than
the dark opening, or " lake," to which I have directed attention,
lying N.W, from the trapezium.
Hardwick Parsonage, Feb, 7, 1866.
P. S. — Having had another opportunity, on February 1 7,
when the weather was favourable, of examining the region S.
of the trapezium with a power of 450, I beg permission to
send a supplementary diagram, in which it will be observed
that an additional "cumulus " has been introduced on the line
of the " frons," according to Sir John Herschel's nomenclature.
The general appearance of this part was as though the "frons"
and " rostrum " consisted of a row of contiguous masses, about
six in number, of which only the three preceding the bright
star 93 were sufficiently insulated to be distinguished sepa-
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Mr, Herschel, Path of a Detonating Meteor. 211
rately. The second and third of these, reckoning backwards
from the S. point, formed an equilateral triangle with a
cumulus in the interior.
The dark rift or channel was not verj distinct on that
evening ; but the opening into which it leads was fairly visible.
I doubted of its continuation beyond the opening through the
nebulosity to the west.
Path of a Detonating Meteor, By A. S. Herschel, Esq.
Shooting-stars, it is well known, are so abundantly ob-
served on certain nights of the year, that already, at the end
of the last century, the term meteorode was applied on this
account to the night of the loth of August. It is suspected
that large meteors also make their appearance on fixed nights
of the year, although not with the same frequency or regu-
larity as the more constant star-showers. Detonating meteors
were observed on the loth of February, 1772, by Brydone; on
the I ith of February, 1850, by the present Astronomer Royal ;
and on the 9th of February, 1865, by a friend of the writer at
Bangalore (S. India); all of which probably belonged to the
same zone of meteors circulating round the Sun.
On the 2 1 St of November, 1865, at 6^ 5™ Gr.M.T., a meteor
about three times as bright as Venus is at its brightest, and
having an apparent diameter of 8' or 1 o', was observed by Mr.
Warren De La Rue near Cranford. The meteor rose from the
eastern horizon, being surrounded at first, like a comet, by a
parabola-shaped halo of light, reminding an observer of the
zodiacal light, in its form, but rapidly rising and becoming
brighter. When at an altitude of about 40° due east the me-
teor emerged like a fire-ball from a roman candle, of a blue
colour, about a quarter of the apparent diameter of the full
Moon in width, and drawing after it a trail of reddish-coloured
sparks, 2f ° or 3° in length. As it passed overhead, the out-
pouring and falling behind of the matter forming the train
became distinctly visible. At Wimbledon, near London, where
the meteor was seen by Mr. F. C. Penrose, it vanished sud-
denly, or at any rate very rapidly, about 8° N.W. of u LyrcB.
No streak appears to have been left, or, if conspicuous, it was
hidden by a haze which generally overspread the sky. An
account of the meteor having been published, and information
from other observers regarding its appearance being re-
quested by Mr. De La Rue, observations from places as far
distant as Liverpool were received, as well as accounts from
places more near to the mouth of the Thames, where the
meteor at first made its appearance in the zenith. From a
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2 1 2 Mr. Herschely Path of a Detonating Meteor,
comparison of these accounts it is possible to determine, at
least approximately, within small limits of error, the real alti-
tude, position, and velocity of the meteor.
The height of the meteor, at the moment of its first ap-
pearance, is determined from six independent descriptions,
each of which, separately compared with Mr. De La Rue's
original observation of the meteor at Cranford, furnishes an
estimate of the real height of the meteor at its first appearance.
The mean of all the separate heights is taken as the real
height; and the average error from the mean of all the
separate heights is seven British statute miles.
The height at disappearance is determined, in an exactly
similar manner, from the same six accounts compared with the
observation of the apparent place of disappearance of the
meteor, as observed at Wimbledon by Mr. F. C. Penrose. The
accuracy of the determination is about the same as in the
former case, or about seven miles, either above or below the
mean. When the nature of the phenomenon is considered, and
particularly the difficulty of fixing the exact position of the
apparent path of the meteor, as seen by the several observers,
it is not by any means surprising that such differences should
exist in the separate observations, but rather surprising that
such good observations could be made.
The meteor of the 21st of November, 1865, traversed the
entire length of the valley of the Thames, — a distance of about
seventy-five miles, — from forty-one miles above the Nore to
twenty-seven miles above the Earth's surface in the neigh-
bourhood of Henley-on-Thames. On the average of four sepa-
rate accounts, estimated by different observers between four
and ten seconds, the time taken by the meteor to travel the
entire distance, about seventy -five miles, was six seconds and
a half. On this estimate the velocity of the meteor, relatively
to the earth's surface, was about eleven miles per second. The
direction of the actual position of the meteor's flight was from
a point in the neighbourhood of the constellation Taurus^ be-
tween Taurus and the head of Cetus, The meteor of the 19th
of November, 1861, about to be mentioned, was observed at
Woodford as at first stationary for two seconds at a point in
Cettis,
The distance of the meteor, at the moment of its disappear-
ance, from Wimbledon, collectively determined from these ac-
counts, is about thirty-six miles. At Wimbledon Mr. F. C.
Penrose heard a loud report, like that of a cannon fired off at
the distance of some miles, distinct enough to be heard very
plainly by one other person at Wimbledon, about two minutes
and twenty seconds after the meteor had disappeared. Sound,
with its ordinary velocity of 1 090 feet per second in common
air, would take two minutes and fifty-four seconds to travel the
entire distance of thirty -six miles from the point of the disap-
pearance of the meteor to Wimbledon. Considering, as before,
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Mr. Hersehely Path of a Detonating Meteor. z 1 3
the difficulty of fixing the exact position of the apparent path
of the meteor, and hence the approximate nature of the real
path concluded from the independent statements of the ob-
servers, the agreement of the calculated time with the time
observed by Sfr. Penrose, between the disappearance of the
meteor and the occurrence of the sound, must be regarded as a
near coincidence. There can be little doubt from this circum-
stance, — from the nature of the sound, the great apparent
brightness of the fire-ball, and from its near approach to the
earth, — that this meteor was really a detonating fire-ball.
Detonating meteors are described in the British Association
Reports as having taken place in England, during the last five
years, very nearly on the same date of the year as the meteor
of the 2ist of November, 1865. The first of these meteors
exploded over Ipswich and Norwich, with three distinct re-
ports, like heavy ordnance or distant thunder, on the evening
of the 19th of November, 1861. The sound of the explosion
of the second was heard at Hallaton, in Rutlandshire, on the
20th of November, 1 864, like distant artillery, lasting several
seconds. Finally, a detonating meteor of unusual size, de-
scribed by Kepler in his Ephemerides (cited by Halley in the
Philosophical Transactions for the year 17 19, p. 978), which
passed over Grermany with a report like thunder, heard in
Austria, on the 17th of November, 1623 (N.S.), may be
thought, with great probability, to belong to the same zone of
meteors encompassing the Sun. The sidereal year exceeding
the length of the tropical year by almost exactly one day in
seventy years, the position of the Earth in its orbit at the time
of the occurrence of Kepler^s meteor (nearly two centuries and
a half ago) would coincide with the Earth's place in its orbit,
at the present time, on the 21st of November; exactly the date
when Mr. Warren De La Rue's meteor was observed.
The epochs of the 9th- 1 ith of February, and the i9th-2ist
of November are, therefore, dates deserving special attention,
partly with a view of determining for the future the directions
of the detonating meteors, and partly as showing, by their fre-
quent return within very narrow limits of time about those
dates, that aerolitic meteors, like the acknowledged star-
showers of August and November, revolved in fixed orbits
round the Sun.
b2
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214 Bev» Father Secchij Spectrum of»Orionis.
Spectrum of « Orionis. By the Rev.
Father Secchi.
I
^ {Extract from a Letter addretted to the Secretary,)
I I take the liberty of sending a sketch of
* ^ drawing of the spectrum of « Orionis, It
has been made with an apparatus of M.
j2 Merz, of Munich, combined with a prism of
I Amici, made by Hoffman. The details are
strong and wonderful, although the prism is
very small. I hope to be able to make new
observations with a larger prism and yet
f greater light.
^ As a point of reference, I mention that
the line ^ is that of sodium, and n that of
magnesium.
There is some considerable difference in
the position of some nebulous bands, as
compared with the figure of Mr. Huggins'.
1 am sure there is no fault in the measures.
I Is there any real change?
^ The spectrum of Sirius is seen with this
instrument most admirably. It appears ail
striated by narrow equal bands, like the
spectrum of Sulphur in the plate of M.
Pliicker, given in the Philosophical Trans-
actions for the year 1865.
I suspected some illusion in these equal
bands, and I looked to Rigely but I found
g that there also are the bands, but much
J narrower, almost as the spectrum of nitrogen
^ in the same plate; 4^ bands of Sirius are
equivalent to 6f of Rigel.
I send you also a photograph of a solar
spot observed on the 1 6th January last. It
will show how the details and veils are seen
with the polarising eye-pieces. The red
colour of some veils vanishes with common
Q eye-pieces, even if diagonal.
^ RomCf Feb. 10, 1866.
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Mr. Huggins and Dr. Miller^ Spectrum of«t Orionis^ 215
Note on the Spectrum of the Variable Star « Orionisy with
some Remarks on the Letter of the Rer, Father Secchi.
By William Huggins, F.R.S., and W. A. MiUer, M.D.,
LL.D.
P. Secchi, in consequence, as he states, of '^ some consider-
able difference in the position of some nebulous bands '' in his
diagram from the figure which accompanies our paper, " On
the Spectra of some of the Fixed Stars,*** asks, " Is there
any real change ?**
A real change in the spectrum of a star, since it implies
either a change in the chemical constitution of the star, or
important physical changes which effect an alteration in the
investing atmosphere of vapours, to the absorptive action of
which the lines in the spectrum are due, should not be as-
sumed, except as the result of observations made with the
extreme care that so delicate an investigation requires. We
do not think that it is possible to determine a question of so
much importance to cosmical science from a comparison of P.
Secchi's diagram with our own, for the reasons which follow.
P. Secchi gives no information as to how many of the
lines in his diagram have been laid down from actual measure-
ment. Into our diagram those lines only were admitted of
which the measures are contained in a table which accom-
panies the diagram. Our figure, therefore, is not intended as
a full representation of the spectrum as it appeared in the
instrument, — for a number of lines, much greater than the
eighty measured lines given by us, might easily have been
inserted, if we had not thought that the 4;rustworthiness of the
diagram would have been impaired by the addition of lines
of which the positions were only estimated. Our measures
were afterwards checked and verified- by the simultaneous com-
parison, in the instrument, of the star spectrum with the
bright lines of sixteen elementary substances. The positions
of several of the brightest lines of each of these elements are
given in our diagram relatively to the measured lines of the
star.
Again, since the relative proportions of the different parts
of the spectrum are affected by the quality of the glass of
which the prisms are made, and also by the positions of the
prisms in relation to the light incident upon them, the diagram
of « Orionis should be accompanied by measures with the
same instrument of some well-known lines of reference, as
the principal lines of Fraunhofer. P. Secchi says that " the
line ^ is that of sodium, and u that of magnesium," but with
these positions the colours placed beneath the spectrum are not
in agreement. In that case, the part of the spectrum under
which " azzuro " is written, would be about E of the solar
* PhU. Trant. 1864, p. 413.
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2i6 Mr. Huggins and Dr. Miller y Spectrum of a Orionis,
spectrum, and on the same scale, the part of the spectrum
above "violetto," would be a little more refrangible than
Fraunhofer's F.
It may be well to mention here that for the measurement
of stellar spectra a very narrow slit must be employed. For
since it is not possible by the clock-motion of an equatoreal
instrument to maintain the image of a star in an invariable
position within the jaws of a rather wide slit, the measures
will not be satisfactory, unless the width of the slit is less
than that of the image of the star made linear by the cylindri-
cal lens, and the passage of the stellar image before the slit
is seen to make no sensible alteration in the position of the
lines of the spectrum.
The spectroscope, with which our measures were made,
has been preserved with its adjustments unaltered. With
this instrument, on the 6th and 1 2th of March, we measured
the more refrangible terminations of the shaded groups of
lines which, in our diagram and table of measures, are denoted
by the numbers 840, 920, 1169*5, 1300*5, 1420. The iden-
tity of our recent measures with those which we made
during the first three months of 1 864, proves that no change
has taken place in the positions of these groups during the
last two years. The " shading as of fine lines " is still seen,
as in our diagram, on both sides of the lines coincident with
those of sodium.
An important change has, however, been recently observed
by us in the spectrum of this star, though not a change in the
position of any of the groups, such as has been suggested by
P. Secchi.
« Orionis is a variable star of great irregularity, both of
period and of extent of change of brightness.* Now we have
recently found that the group of lines and " shading as if of
fine lines** terminated *at its more refrangible end by the
strong line. No. 1069*5 in our diagram, is not at present
visible in the spectrum of the star. The absence of this group
is of great interest in connexion with the variability of the
star's light, especially as the time of the disappearance of this
group coincides with the epoch of the maximum brilliancy of
the star.
Since we might be biassed in our estimation of the present
degree of brilliancy of the star, by our knowledge of this
peculiar change in its spectrum, one of us wrote to Mr. Baxen-
* Sir John Henchel writes : — ** The variations of « Orionit whick were
most striking and unequivocaly in the years 1 836-40 , within the years since
elapsed, hecame much less conspicuous. In Jan. 1849, they had recom-
menced; and on Dec. 5, 1852, Mr. Fletcher observed « Orionia brighter
than Capella, and actually the largest star in the northern hemisphere 9 Out-
lines of Astronomy, p. 6oz. Until the present time, the changes of this
star appear to have been again inconsiderable. See Schmidt, Ast, Naeh» No.
1570." -
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Mr, Hoggins and Dr. Miller^ Spectrum of » Orionis. 217
dell, whose successful prosecution of this branch of astronomy
is 80 well known, requesting him to state in what phase of
its period of variation x Orionis is at the present time. His
reply is as follows: — *' March 9, 1 866. The variable « Orionis
is irregular both in the extent of its variation, and in the
duration of its period. It has been increasing in brightness
since the end of December, and is now at, or very near, a
maximum. I have often thought that its light was at times
variable in colour as well as intensity, being sometimes very
perceptibly more ruddy than at others. It is, however, a
difficult star to observe, owing to its brilliancy and its ruddy
colour, which is differently acted upon by haze or moonlight
to that of a white star."
The variation in colour, so well described by Mr. Baxen-
dell, corresponds exactly to the change in the colour of the
star, which would be produced by the absence or presence of
the group of lines of which we are speaking, since the position
of this group in the spectrum is about the. boundary of tho
" orange " towards the " yellow."
We have been for some time occupied with observations of
other variable stars, which we believe may give to us new
information of the probable mode in which, in some stars at
least, the periodic alteration of light of these remarkable ob-
jects is brought about. We should, therefore, have much
preferred reserving, for the present, our observations of the
remarkable fading out of this group of lines in the spectrum
of cc Orionis, We may mention here that the fine lines in the
spectra of Sirius and Rigel, referred to by P. Secchi, were
described by us in our paper read before the Royal Society in
May, 1 864, in the following words : —
" Sirius. The spectrum of this brilliant star is very in-
tense, but owing to its low altitude, even when most favour-
ably situated, the observation of the finer lines is rendered
very difficult by the motion of the earth's atmosphere
Three, if not four, elementary bodies have been found to fur-
nish spectra in which lines coincide with those of Sirius, viz.
sodium, magnesium, hydrogen, and probably iron The
whole spectrum of Sirius is crossed by a very large number of
faint and fine lines It is worthy of notice that in the
case of Sirius^ and a large number of the white stars, at the
same time that the hydrogen lines are abnormally strong as
compared with the solar spectrum, all the metallic lines are
remarkably faint."
*' Bigel, A spectrum full of fine lines."
The appearance of these fine lines is not such as to suggest
to us any resemblance to those spectra of sulphur and nitrogen
which are referred to by P. Secchi.
* Phil. TYans. 1864, pp. 427, 428,429.
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21 8 M, Brunnow, Ephemeris of Iris
Occultation of i^o Tauri, By C. G. Talmage, Esq.
1866, February 23. Occultation of 130 Tauri.
G.M.T. of Disappearance,
- 5** 30" 5i"73-
Star rather faint.
G. M. T. of Reappearance,
ss 6*» 13"" 54"'26.
Came out exceedingly bright and sharp for a 6th mag. star ; time exact.
Note on the Companion to Antares. By D. A. Freeman, Esq.
I beg permission to say that, on turning my Cooke's 4|-in.
refractor on Antares an hour before sunrise, on the 2 2d inst.,
the atmosphere being in an exceptionally fine condition, the
small ^tar was very clearly visible, and, at times, quite free
from the light round the large star. The colour of the small
star appeared to be green; and, with a negative eye-piece
naagnifying 180, I kept it steadily in view till the Sun had
appeared upon the horizon.
This star being clearly visible with a small object-glass of
4f inches makes it a matter of surprise that it should have
been discovered but recently, only though, from its low
declination, it is probably more difficult to see it well in
England than in this latitude.
Mentone, Alpes Mariiimea, Jan. 24, 1 866.
Ephemeris of Iris for the Opposition ofiS66.
By F. Brunnow.
The following Ephemeris for the opposition o£Iris has been
calculated by me from my Tables. In constructing these, the
perturbations of the first order produced by Jupiter, Saturn,
and Mars, as well as the terms depending on the square of th^
mass o£ Jupiter, have been taken into account. As the ellip-
tical elements of the orbit are pretty accurately known, I
expect that the error of the Ephemeris will be small, and that
the tables will give the planet's place with sufficient accuracy
for a long time to come. They represent six normal places
distributed over a space of eighteen years very satisfactorily,
the errors being as follows : —
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for* the Opposition ofiS66.
219
a2.
1847 Aug
. 20-0
+ 0*27
+ 1-98
1851 Oct.
3*5
-0-25
-1*71
1855 ^^
14-5
+ 0-05
+ 0-51
i860 Feb.
8-5
+ o-o6
+ 0-85
1862 Sept
.11-5
+ 0*12
+ 1-33
1865 June io'5
-0-25
+ 0-71
Ephemeris for Berlin Mean Midnight.
Hourly
Motion.
Hourly
Motion.
Log
Distance.
h m 8
/ «
Nov. 18
4 59 38-24 -
-2-052
+ »5 »5 59*5
— 13-82
9-95950
"9
58 48-18
2-116
25 20 24*0
14*12
9-95847
20
57 56-66
2-175
25 14 41-5
14*41
9*95755
21
57 3*77
2-230
25 8 52-3
14-69
9-95674
22
56 9*62
2-280
25 2 56*5
14*96
9-95604
»3
55 15*30
2-327
24 56 54*4
1522
995544
*4
54 i7-9»
2-369
24 50 46*2
15-46
9-95491
as
53 ao-57
2-407
24 44 32-2
15-70
9*95457
26
52 22-36
2-441
24 38 12-8
1592
9*95430
27
51 23-40
2-469
24 31 48-2
16*12
9*954»5
28
50 23-84
2-491
24 25 18-9
16*31
9-95410
29
49 ^3-8*
2-508
24 18 45*1
16-49
9*95416
30
48 23-44
2-521
24 12 7*4
16*64
9*95434
Dec. I
47 22.- 82
2-527
24 5 26*2
16*78
9-95463
2
46 22*11
2-529
23 58 41-8
16-91
9-95504
3
45 »i*44
2-525
23 51 54*7
17-01
9*95556
4
44 *o-93
2-515
*3 45 5-4
17-09
9-95620
5
43 20-70
2-500
23 38 14*3
17-15
9-95695
6
42 20-90
2-480
23 31 22-1
17*19
9*95782
7
41 21-64
»-455
23 24 29-3
17*20
9-95881
8
40 23-07
2-424
23 17 36-3
17-20
9-95990
9
39 *S'a9
2-388
23 10 43-8
17-17
9-96110
10
38 28-42
2-348
23 3 52-3
17-11
996241
11
37 3*-58
2-303
22 57 2-3
17-04
9-96384
12
36 37-88
2-253
22 50 14-3
16-95
9*96537
13
35 44-4»
2 -200
22 43 28-7
16*84
9*96701
>4
34 5a'*9
2-142
22 36 46*1
16-70
9-96875
^5
-34 1-61
2-080
22 30 7*2
16*54
9-97059
16
33 "-45
2*015
22 23 32-2
16*36
9-97253
17
32 24-88
>-947
22 17 1-7
16-17
9*97456
18
31 38-97
1-876
22 10 36-2
15-95
9*97669
19
30 54-81
l-802
22 4 l6*I
15*71
9*97890
20
4 30 12-48
-1-725
+ 21 58 2-0
-I5-45
9*98121
Dunsinky Observatory of Trinity College, Dublin,
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220
ERRATA.
Page 144, line 5 from bottom,/or 190 H. II., read 199 H. II.
— — — 9 — /or 51 H. I., r«ttJ 52 H. I.
— — — 15 — ybr 38 H. IV., rcflJ 38 H. VI.
— — — 8 — omit 4627 192 H. I.
— 150, — 12, for Arlem, read Anclam, Pomerania.
CONTENTS.
Page
Fellows elected .. .. 103
Investigations on Airy's Double-Image Micrometer, by Prof. Kaiser ib.
■ Additions to the Investigations on Cometary Systems, by M. Hoek 204
Notice of the Great Nebula in Orion, by the Rev. T. W. Webb . . 208
Path of a Detonating Meteor, by Mr. Herschel . . . . . . 211
Spectrum of « OrioniSf by the Rev. Father Secchi . . ... . . 2 14
Note on the Spectrum of the Variable Star a Orionie, with some Re-
marks on the Letter of the Rev. Father Secchi, by Mr. Huggins
and Dr. Miller . . . . . . ..215
Occultation of ] 30 Tourf , by Mr. Talmage .. 218
Note on the Companion to Aniarea, by Mr. Freeman . . . • . . ib.
Ephemeris of Irii for the Opposition 1 866, by M. Brunnow . . . . ib.
Printed by Stbanobwats and Walden, Castle St. Leicester Sq. and Published
at the Apartments of the Society, April 7, i860.
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University c
MONTHLY NOTICES ^-^^IB}^
OF THE
ROYAL ASTRONOMICAL SOCIETY.
Vol, XXVI. April 13, 1866. No- 6.
Rev. Chables Pbitohard, President, in the Chair.
Edward John Routh, Esq., Cambridge ;
George Hurst, Esq., Edgbaston ;
H. Emerson Westcar, Esq., Royal Horse Guards, Knights-
bridge; and
Charles Victor De Santy, Esq., 34 Radnor Street, Chelsea,
were balloted for and duly elected Fellows of the Society.
On the Supposed Possible Effect of Friction in the Tides, in
influencing the Apparent Acceleration of the MoorCs Mean
Motion in Longitude, By G. B. Airy, Astronomer Royal.
Our illustrious Associate, M. Delaunay, has lately made a
communication to the Institute of France, in which he explains
a portion of the apparent acceleration of the Moon as possibly
due to a real retardation of the rotation of the Earth, and con-
ceives that such retardation may possibly arise from friction in
the tidal movement of the waters. In suggesting this explana-
tion, he lays down as fundamental theorems (as I understand)
the two following: — First, that, if the solid globe of the Earth
were covered with water, there would be high water under the
Moon (considered as the only tide-producing body) ; secondly,
that the effect of friction would be to make the semi-diurnal
tides later than they would be if there were no friction.
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222 Astronomei' Royal, on a Supposed Possible
Any treatment of the tides is, necessarily, very imperfectly
applicable to the real motion of the waters, under all their com-
plicated circumstances of unsymmetrical boundaries, varying
depths, and unknown laws of friction. Still attempts have been
made, upon different hypotheses admitting of mathematical
treatment, by which the different points of M. Delaunay's
theory may be tested. The attempts to which I refer will be
found in the following works : —
I. Newton, Principia, Lib. I. Prop. 66, Cor. 1 9.
II. Laplace, Mecanique Celeste; cited also and reinvesti-
gated in Encyolopcedia Metropolitana, Tides and Waves,
Art. (109), &c,
III. Airy, EncyclopcBdia Metropolitana, Tides and Waves,
Art. (281) and (325).
Newton's fundamental supposition is that of a fluid ring
equatoreally surrounding the Earth ; Laplace's, that of a fluid
completely covering the Earth, on two suppositions of depth,
of which one admits of complete solution and the other admits
of imperfect solution ; Airy's (among various suppositions),
that of a fluid equatoreal ring, in which the motion of the
waters may be supposed, either to be unaffected by friction, or
to be affected by friction proportional to the velocity of mo-
tion (a law of friction which will certainly represent with great
accuracy the general effects of fluid friction). And the results
of the comparison of the theoretical inferences from these prin-
ciples with M. Delaunay's assumptions are very remarkable.
They are all in direct contradiction to these assumptions, and
to M. Delaunay's further deductions : —
IV. Newton, Laplace, Airy, agree in this, that there will
be low water under the Moon. In a subsequent part of
the Principia, Newton thinks that the high water would
in some measure follow the Moon's place.
V. Airy shows that the effect of friction is to accelerate the
time of each individual tide.
VI. It is a result of this friction that the velocity of the
Earth's rotation is not affected,
VII. It is a further result of this friction and the conse-
quent disturbance of the form of the waters that the
Moon's motion is affected ; her orbit is made to become
large, and her motion in longitude is retarded.
The interest now attaching to these points is so great thai
I may perhaps be excused, even at the risk of repeating an in-
vestigation already published, in giving the principal steps of
my own process. It possesses the advantage, which at the
present moment is of the utmost value^ and which is ^ot pos-
sessed by any of the other investigations^ of including the
effects of friction. The results which I have marked (VI.) and
(VII.) are new.
The subject of investigation is the motion of the waters in
an equatoreal canal of uniform depth ; the rotation of the
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Effect of Friction in the Tides. 223
Ehtih, ftDd ihtf Moott*^ ftHgulslr I'evolution, find (Sditseqtimitljr
tbe Mooned change of hour-angle» being uniform. The Moon's
distance i§ supposed to be invariable, and her declination either
o or invariable*
It is eadily showh thai in thid <ias6 the motJoU obtained by
supposing the Earth at rest and the Moon revolving With her
hour-angle velocity will be the same as that corresponding to
the real circumstances (as, indeed, is alwavs assumed).
Adopting some one point of the canal as zero of measure,
let ar, measured westwardlj from that point, be the abscissa
for any point of the fluid under consideration ; y the similat
abscissa fof the point to which the Mooli is v^rticsd. If t* be
the Earth's radius, the angular distance of the Moon westward
from the meridian of the point x will be - - -. Then it is
a. If, ^
known from the ordinary theory of perturbation that the hori-
zontal force produced by the Moon on particles in the place x
and its neighbourhood may be represented by H sin * (^ " ~y
(it is shown in Tides and Waves, article 279, that the eflfect of
the vertical force is insignificant). The measure y is propor-
tional to the time, and therefore the expression of this force
may be put in the form + H sin (t ^ — m a;) ; the positive sign
bdag used because, when sin 2 ^^ - -) is positive^ the force
fends to move the water in the direction in which x is mea-
sured.
A second force is derived from friction. Suppose that the
mean abscissa for any particle is Xy but that its true disturbed ab-
Digiti
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224 Astronomer Royaly on a Supposed Possible
scissa at any moment is a; + X (X depending on, or being a func-
tion of, X and t). Then the velocity of the particle is -^. And,
supposing the friction proportional to the velocity, and the direc-
tion always opposed to the direction of motion, it may be repre-
sented by — / -jT-.
A third force depends on the form of the surface of the
water. Let the mean depth of the water be k. Then, in the
mean state of the water, the volume included between the
points whose mean ordinates are x and a; + ^ x, is A ^ re. But,
in the disturbed state, x is changed to a; 4- X and x ■\- ^xis
changed toa; + ^a; + X + ^ — ^x ; the distance between the
I + ^ ) ; and, as the volume ^ ^ a; is still
included between them, the depth of the water now is
Jx~^C'~^y nearly, or its surface is raised by
— k -7— nearly. This is the tidal elevation of the point whose
mean abscissa is x. The tidal elevation of the point whose
mean abscissa is a; -f A will be — A (3— + A 3— . -r-h or
\djp da dx /^
— k^ kh T-r. The excess of the former is + ^ A -j—w.
dse dap* Jar
This is the height of a head of water which acts horizontally
upon the whole depth k of the water, and of which therefore
the entire pressure is + k^k -r-i • The volume of water on
which it acts is h h. Hence, by the usual rule connecting
pressure with accelerating force, the accelerating force de-
pending on this cause is + ^ A j^.
Collecting these three accelerating forces, and forming the
usual equation of motion, and remarking that the abscissa to
which the motion really applies is a? -f X, but that, as a; is in-
dependent of ty the expression ^ ^ — -' is really j-j ;
^X ^ XT • /w X /. rfX , d«X
It is impossible (in our present state of mathematical
knowledge) to give a general solution of this equation ; and it
would be useless if we could give it, because it must include
every ripple on the sea. But a solution, of the utmost gene-
rality in its reference to the periodic forces which produce the
tides, will be obtained by the following assumption of corre-
sponding periodic character: —
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Effect of Friction in the Tides, 225
Let X s A . sin (t < — mx) + B . cos (t < — m»)\
and substitute this for X in the left-hand term and in two of
the right-hand terms of the equation. We obtain immediately,
o = {i«A + H +/iB - ^*i»« a}, sin (« /-!«*)
+ {i«B -/«A-^*'»'B} .co8(»/-m*):
and, as each of these terms must separately = o,
o = (»•«- ^*m*) . A + /i . B + H,
o« (.•»-5r**»«).B-/i.A;
from which,
and
If the constant angle F be determined hj the equation
tan F = ^_ ' a ; where, with a positive denominator, F
will always be positive and less than 90®; then
oosF^ tjLllLat ,8mF ^1
and the expression for X becomes,
— H
^"^ yf(j^_yj^^«)«+y«,-«i '{8iPC><-w«Jf).co8F-l-co8(«^-may).8inF}
B zJ! . sin (« / + F — m Jp).
/ETC
The tidal elevation of the surface of the water, or — A -r—.
18
-mH .k
y{(?-5r*m«)» +/»!»}
. oo8(f< + F — m*).
Digiti
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226 Astronomer Royaly on a Supposed Possible
If there urere no frictiofi, /ess o, F s o, and we should
have, '
X without friction = ^ '^ , sin (< ^ — in ^] ;
— tn TT it
Tidal Elevation of Si:^rface wit^^Q^t fnction f! = — *» y , qos (t ^ — m ;p) .
In order to arrive at a proper understanding of the import
of these expressions, it is necessary first to ascertain whether
gkm^\A greater or less than C'.
Now it will be remarked in a preceding sentence that it
has been assumed that v is proportional to the time, saj = n ^,
in which assumption it is obvious (on inspection of the first
diagram) that n is the nuipber of units of linear measure on
the Earth's equator over which the Moon passes in a unit of
time, and t/ or — is therefore ^-^, and % is — ; where n
exceeds lopo miles per hour, or )40q feet per second. The
value of »» is -. And ^A is the product of 32 by the depth
of the sea in feet (always using the foot and the second ^
the units of measure and time). Thus
«' — ^*»»* — 3 { i8oo\* -- 118 X depth of sea in feet }.
This quantity will alwajrs be positive except the depth of
the sea exceed 1 2 miles ; far exceeding any supposed real
depth of the sea. The denominator i^ 1^ pk m^ therefore is
always to be considered positive.
Now when the Moon is vertical ov^r any point x of the
can^l, t/itr^x (s^e thQ diagram) fr o^ eir a ^^ -r ? j = o, or
t/ — wia; = o. Therefore, if there be no friction, the tidal
«n TT it
elevation of the surface = — . u ■ ■ ^ «; x coa d. This is its
P — g knr ^
maximum negative value. Consequently, it is low water under
the Moon.
Also, if the term ffkm^in the denominator b^ neglected,
the tidal elevation (which has k for a factor) is proportional
to the depth of the sea.
Theorems equivalent to these were proved by I^aplj^oe.
K there be friction, the tidal elevation of the watCF is
— D . cos (t ^ + F — 7» x), (D being the coefficient above).
This quantity h^ }t^ greatest negf^tive y^lue, o^ \\ \^ low
water, when it -{- F — »» a? = o, or when t = 2£JI1— . If ther^
had been no friction, low water would hav^ pc(j\jrred when
mx
t=z --r-. The former value of t is the smaller } and therefgre
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Effect of Friction in the Tides.
zzy
the phase of low water {and consequently the other phages of
the tide) are accelerated by the friction.
The magnitude of the tide is evidently diminished (but
constantly, not varying from day to day) by the friction;
its denominator being >/{(»* — ^^ »»*)* + /* t*} instead of
i* — gh «»*.
The value of friction upon the water at any place x is
— f ---rri ^^^ therefore the reaction of the water's friction
upon the solid channel is + / . -^ , or
^{(t»-^*m«)» +/».»} COB (»/ + F -m^).
To obtain the effect of this on the entire solid globe, we must
integrate cos (t f + F — wi a;) or cos (t ^ + F — - a;) with re-
spect to a;, from a; = otoa;s=2r9r. This definite integral is
obviously =: o ; and therefore the friction does not tend at any
instant either to accelerate or to retard the rotation of the
solid globe.
This result, it will be seen, depends on considerations of
the first order only of the disturbing force. The treatment of
results to the second order is extremely diflScult, and I am un-
able to say what conclusion would be derived from them. At
present it appears desirable to establish, with as much accu-
racy as the nature of the case permits, the results of the first
order.
Yet the friction does produce an efiect on the motion of
the Moon. We have found that, at the place a;, the low water
occurs when t = — : — , or when y or — = - (m x — F),
= -(— — F ) =a; ^. That is, at low water the Moon
is east of the meridian, or in the former diagram is to the left
of the radius passing through the place of low water, by the
F ._
angle - . The relative position of the Moon and the elliptic
water-channel may therefore be represented •^^^m.
by this second diagram. The attraction of
the protuberance at P tends to draw the
Moon transversely to the radius -vector,
towards the left. The attraction of the
protuberance at Q tends to draw the Moon
transversely to the right, but by a smaller
quantity. On the whole therefore the at-
traction transversal to the radius vector is
to the left, which is the direction of the
Moon's real motion. The attraction there-
fore accelerates the Moon's linear motion in
its orbit i in consequence of tbiis the Moon's
Digiti
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228 Astronomer Royal^ on a Supposed Possible
orbit is continually growing larger, and therefore the Moon's
angular motion is diminished ; or the friction of the tides
produces a retardation of the MoorCs mean longitude.
It would seem probable that the reaction, on P and Q, of
these forces, will in some waj produce a retarding effect on the
Earth's rotation. There are other instances in the lunar theory
in which the Moon's action on the equatoreal protuberance
of the Earth is accompanied by action of that protuberance
on the Moon, both producing well-recognised effects. But in a
case like this before us, where the very existence of the force
depends on friction and consequent disturbance of the law of
vis viva, I do not profess myself able to follow out all the con-
sequences.
Still it is to be remarked that the force, here spoken of, is
of a higher order in respect of the fraction ^ — r-r-t tban
o ^ Moon 8 distance
the quantities of which the preceding theory treats ; and a
more complete investigation will be required before we can
pronounce with certainty on the tendencies of the forces to
produce secular motions.
It will probably be difficult to say what is the effect of
friction in more complicated cases. Conceive, for instance (as
a specimen of a large class), a tide-mill for grinding corn.
The water, which has been allowed to rise with the rising
tide, is not allowed to fail with the falling tide, but after a
time is allowed to fall, thereby doing work, and producing
heat in the meal formed by grinding the corn. I do not doubt
that this heat is the representative of vis viva, lost somewhere,
but whether it is lost in the rotation of the Earth or in the
revolution of the Moon, I am quite unable to say.
The theorem, that when water moves without friction it
will be low water under the Moon, is so interesting that I may
perhaps be excused for giving a geometrical proof of it
(hitherto unpublished). The method of proof will be : — To
assume that the ring of water has an elliptic form, the elliptic
shape (not the water) travelling round with the same angular
velocity as the hour-angle velocity of the Moon, and that the
motion of every particle of the water is oscillatory ; to examine
more precisely the laws of the oscillatory motion of the waters
in different parts of the elliptic ring ; to investigate the forces
which are required for maintenance of these oscillatory mo-
tions ; and to show that those forces are such as to correspond
to low water under the Moon, and to no other relative position
of the tide and the Moon.
First, it is to be carefully remarked that the rising of the
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Effect of Friction in the Tides, 229
water at any place does not depend on the horizontal move-
ment of the water at that place, but on the relative values of
the horizontal movement on the two sides of the place. If the
water on both sides of that place is flowing towards that place,
the water rises there. If the water on one side is flovring
rapidly towards it, and the water on the other side is receding
slowly from it, the water rises there. When the surface at
any one place is stationary as to height, there may neverthe-
less be considerable horizontal velocity ; only it is certain that
the water is flowing towards it on one side exactly as fast as it
is receding from it on the other side.
Now in this third diagram let the strong elliptic outline
represent the form of the surface of the water at the present
instant ; and let the dotted line represent the form which it
will take in a short time ; the form of the dotted curve being
the same as that of the strong line curve, but having turned
round with the same angular velocity as the Moon.
At A, C, E, and G, the height of the water has scarcely
altered from the state of things with the strong outline to the
state of things with the dotted out- .^
line. Therefore, the speed of the
water is equal on both sides of each
of these four points. And therefore
it will readily be understood from
the ordinary theory of maxima and
minima that at these four points the
horizontal motion of the water is
most rapid: its direction at each
being at present undecided.
At B and F the water is rising
most rapidly ; therefore the water is
flowing from both sides towards B
and towards F. ''^
At D and H the water is sinking most rapidly ; therefore
the water is receding on both sides from D and from H.
Hence it follows that the directions of currents are repre-
sented by the arrows in the diagram.
We have now obtained complete knowledge of the state of
the currents in the strong-line ellipse. And from these we
can infer the state of the currents in the dotted-line or subse-
quent ellipse, remarking that in this subsequent case the sub-
sequent currents maintain the same relation to the axes of the
subsequent ellipse which in the preceding case the preceding
currents held to the axes of the preceding ellipse. And, by
comparing these, we shall learn what are the changes made
in the currents at each place, and what must be the forces
which produce these changes.
In this fourth diagram —
At A, C, E, G, the current is scarcely changed, or the
forces are o.
Digiti
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230 Astronomer Boyaly on a Supposed Possible
At B a current o is changed to ^^ and a current ^ is
changed to o, or the force is ^k.
At D a current o is changed to 4^, and a current ^ is
changed to o, or the force ims^. -
In like manner, at F, the force is t^ ; and at H the force
is ^.
O
-^
These forces are such as are produced by the Moon in the
position shown in the diagram, or in the opposite position;
and in no other position. Therefore it is lota water under the
Moon,
In this investigation it is to be remarked that I have not
jet taken account of the pressure produced hy the head of
water at C and G. Its tendency is exactly the same as that
of the Innar forces, namely, to push the water both from C and
from G towards both A and E. It therefore does not alter
the law of tides, but merely requires a smaller agency of the
Moon to produce a tide of given magnitude. In other words,
the tide is rendered larger by this consideration.
Appendix.
Since presenting this paper to the Secretary of the Society,
I have endeavoured to extend the investigation to higher powers
of small quantities. As far as applies to another power of p (the
quotient of Earth's radius by Moon's di&tance) there is no ^ffi-
culty ; the dragging force of the Moon on the waters is repre-
sented by H X { sin a hour-angle + "i i> . ain hour-angle
+ f p . sin 3 hour-angle] ; the first and second of these terma
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Effeet of FrioHan in the Tides. 231
produce terms in the elevation of the water with /for factor,
and depending on sin 2 hour-angle and sin hour-angle ; and
these t^nns when multiplied by {p • sin hour-angle + f 77^
sin 2 hour-angle) to give the amount of force accelerating the
Moon in her orbit (and therefore retarding her mean longitude)
gir^ two additive constant terms. The term resulting from
the product of the term of elevation depending on sin . hour-
apgle by the fkctor^ . sin hour-angle^ appears to me to corre-
spond to the displacement of the centre 01 gravity of the united
mass of nucleus and water, and therefore it appears to produce
no effect in the Moon's ipotiou round the centre of gravity.
But there is no displacement of the centre of gravity corre-
sponding to the terms depending on sin . 2 hour-angle ; and
those terms (ippear to me to produce a real effeot 00 the Moon's
motion.
The terms introduced by the higher power of p do not
produce any expresslQi) of fractional retardation in the rotation
of the Earth's nucleus.
As far as applies to a higher power of the force^ or (which
in the investigation becomes equivalent to it) a higher power
of " tidal elevation divided by depth of sea," the following in-
vestigation is given, rathei* for the purpose of showing how the
dSbct of the finite proportion of tidsd rise to the depth of sea
may mathematically be taken into account, than for the general
conclusion, which may be obtained by pimple reasoning. The
introdnqtion of the higher powers of p producer great com-
ptewty and adds npthing to the value of the reaultj and I shall
therefore owit them.
The friction between the water and the nucleus, as affecting
the motion of the water, h^9 been ex;presa6d, aa an accelerating
force, by the symbol — /-jr* I** expression as a moving
force, on the quantity of fluid which originally occupied the
space between x and x + ^a;, will be — /-jr X ki x. The
summation of thi^ for the whole qbannel (which, with sign
changed, gives the action upon the nucleus) will require us
J Y
simply to integrate ^f^Tt ^^*^ respect to a?. It is only
necessary therefore to examine whether -jj can contain any
non-periodic term.
The depth of water is expressed by
M'-Sf'(lf)T
The tidal elevation, for the part whose original ordinate was s^,
is A j -r- — + (5-^ i I • That for the part whose original
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232 Astronomer Royal^ on a Supposed Possible
ordinate was a; + A, is
*{-5J-5^*+ WV^rfJ-IS^-^l-
The excess of the former is kh |^- »1| . ^| . The
pressure of this head of water acts on the ^uid through the
whole depth ; and its entire pressure is therefore, whole depth
X A A I — f— »_ . ~— . I . The mass of water to be moved
is k h. Therefore the accelerating force is,
w k 1 J *i. i^X rfX <rx )
g X whole depth x i^-*^^ "^\
Hence, the equation of motion will become,
<px „ . ,.^ , -dx ^d«x ^dx <rx
in which the last term is considered as small.
It does not appear practicable to solve this equation except
by successive substitution; first solving the equation without
the last term, then substituting in the last term the value so
found for X, and thus producing new functions of t and x to be
annexed to H . sin (« ^ — »i x\ by which a new equation will
be prepared for solution in the same manner as the first.
Taking then X = A . sin (t / — »* a?) + B . cos (t7— wire), where
A and B have the determinate values already found :
<iX
-J — » — m A . cos (t ^ — m a?) + m B . sin (t / — m x);
-7-3- = — m' A . sin (f / — m « ) — m' B . cos (f / - »i 47),
their product is
}OT»(A«-B»).8in(at/ -»«•*)+ m«AB.cos(at *- im*),
and the equation of motion now is,
— 3^*m' A B .cos(2t^ -am^r).
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Effect of Friction in the Tides. 233
On solving this in the same manner as before, it is evident
that the expression for X will contain only sines and cosines of
it — mx and zit— zmx, and therefore -^ will contain only
similar terms; and the integral of /A , -^ through the whole
circumference = o. This, with sign changed, is the moving
force tending to retard the sphere's rotation ; and therefore, to
the second order of disturbing forces inclusive, the friction of
the tides does not tend to retard the rotation of the earth's
nucleus.
But the aggregate effect, as obtained here, may also be
found from the following simple reasoning: — If the friction
vary as the velocity, the whole force impressed on the nucleus
by a given portion of the wat-er in passing through a certain
space is exactly proportional to that space, and an exactly
equal force will be impressed in the opposite direction by
returning through the same space ; and thus, in the most com-
plicated case of oscillating motion, if at any time the particles
return to the same position as at first, the frictional effect is o.
K the force vary as the square of the velocity, the diffi-
culties of mathematical treatment appear to be almost insu-
perable ; the frictional function being discontinuous, changing
its sign whenever the complicated function which expresses
the velocity becomes o. We can, however, assert that if the
velocity in the + direction and that in the — direction follow
the same laws, the aggregate frictional effect will be o. This
will certainly hold if the terms of the second order of /> be
omitted j but it seems doubtful whether it will hold if they be
retained.
1866, April 3.
Addendum.
1866, April 5.
I have at length discovered two terms which appear to
exercise a real effect on the rotation of the Earth.
First. The coefficient of horizontal forces, which I have
designated by H, is not constant, but is proportional to the dis-
tance from the Earth's centre. If we take that value which
corresponds to half the depth of the water, the true value or
H' may be represented nearly by
Hx I I +-^ tidal rise i
orH X ] I .-777^3 — ^, .va ^ xa -2^ cos (</ — »!* + F) I
Digiti
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Z34 AstranorHef Roylt on a Supposed Passible
imd the true horizontal force» or -f H' « sin (i < -~ m dkf)^ wiU be
H . sin (t < — mj?)
Giring to sin F its ralue, this contains the constant term
mWkfi
Second. The ordinate of the water on which the force is
acting is not x but a?+ X ; and therefore, instead of using the
expression H . sin (it-^ m x\ we ought to use
H • sin (t < -^ mx - mX)«
or
H . sin {it — ma;) — mHX . cos (t^ — mx).
Patting for X its valae, the last term becomes
which, with similar expansion, and substitution for F, gives
the constant term + a f (t^ - g it >»»)« +ni'V "^^^^ *®^°^ ^® much
larger than that found above.
Call the sum of these two terms + c. Then the equation
of motion, as applying to this term only, and putting ft* for
gk, becomes -jji— ft*. -^^ = +0.
Let bt-^x=sUibt^»T:^v; thea this equation may be
changed into
Or, X«-p(ft?/»-^) + ^(ft/-*) -h^ibt + x).
For determining the form Of the arbitrary functions, we
remark that the final solution must contain no power of x
(otherwise we should have inconsistent values in conipleting
the round of the circle), and that the form of the first term
Digiti
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Effect of Friction in the Tides. 235
then admits only algebraical fanctions. Thus we find that the
solation must be,
That is, there is a constant acceleration of the waters as fol-
lowing the Moon's apparent diurnal course. As this is oppo-
site to the direction of the Earth's rotation, it follows that
from the action of the Moon there is a constant retarding
force on the rotation of the water, and therefore (by virtue of
the friction between them) a constant retarding force on the
rotation of the Earth's nucleus.
If, as in the preceding cases, we include in the equation
the term depending on /, the form of solution is somewhat
modified, and a better view of the effect of the new term is
obtained. Remarking that, as is stated above, no powers of x
can be admitted, we may omit -j^ ; and the equation^ as re-
gards the new term, becomes.
The solution of this equation is
from which the friction
Whatever, therefore, be the primary state of things, the
second term will ultimately become insensible ; the frietional
force on the water will be — cm the direction of the Moon's
apparent diurnal motion, or + <: in the direction of the Earth's
rotation ; and this implies a force ^ c in that direction upon
the nucleus of the Earth, constantly retarding its rotation.
I am very happy to give my entire assent to the general
views of M. Delaunay on the existence of one real cause for the
retardation of the Earth's rotation.
G. B. AiRT.
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236 Astronomer Royal^ on a Method of
On a Method of Computing Interpolations to the Second Order
without Changes of Algebraic Sign. By G. B. Airy,
Astronomer Royal.
In the year 1847 I saggested (in a paper printed in the
sixteenth volume of the Memoirs of this Society) a form of
computation by which the troublesome changes of sign in
Bessel's method of computing star-reductions might be com-
pletely avoided.
Using capital letters for numbers depending on the day,
and small letters for numbers depending on the star's place, it
is known that the star-reductions in R.A. and N.P.D. are
expressed by formulae of this character: —
Aa + BJ + Cc + Dd;
Afl' + B*' + Cc' + Dd';
in which formulae every one of the twelve symbols, of their
eight products, and of the two aggregates, may be positive or
negative.
For the numbers A, a, a\ &c., I suggested a series of num-
bers E, c, c', &c., by use of which the star-reductions in R.A.
and N.P.D. are expressed by the following formulae : —
Ee + Vf + Gff + Uh +L + /— 3oo«-ooo
Ec' + F/' + Gy' + HA' + L + ^- 3oo"-ooo
in which formulae every one of the fifteen symbols, of the
eight products, and of the aggregates preceding the number
— 300*000, is essentially positive; the only exception being in
the numbers e,f g^ /i, /, for a very few stars near the pole (not
exceeding in number one in a hundred and fifty for an ordinary
general catalogue of stars), which sometimes make one of the
five symbols negative.
This system was soon brought into use at the Royal Ob-
servatory, and with perfect success. The amount of mental
effort required by the computers of lower class who usually
make the calculations, and by the assistants of higher class
who examine them, is most materially diminished. The most
fertile source of errors is at once taken away.
The success of this system for star-reductions, confirmed by
the experience of many years, induced me to attempt a similar
change in the form of interpolations with second differences ; a
subject of great importance in the calculations at the Royal
Observatory. Our annual interpolations are more than three
thousand in number ; and, since I took the superintendence of
the Observatory, I believe that the whole number has ap-
proached to eighty thousand. Every one of these (before
Digiti
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Computing Interpolations Sfc. 237
making the change which I am about to describe) was liable
to the uncertainties of sign in the first power of the time, in
the first difference^ in the second difference, in the numbers
which they respectively produce, and in the steps of their
aggregation with the ephemeridal quantity; and experience
had shown that the greater number of errors in result arose
from errors in these signs.
I shall now explain, first, the process which had been long
used at the Observatory, and secondly, the steps of improve-
ment by which it was changed to the form finally adopted.
If we take from the Ephemeris the values x^, a^, a?j, corre-
sponding to the equidistant times T^, T^, T, ; and if we wish
to compute the value of x' for the time T^ 4- t (where r is
expressed by a number whose unit is T^ — T^ or Tj — T^,
and is always less than + i, and practically always less than
± i), we begin by taking the differences, thus: —
First Differences. Second Difference.
Then, forming the coefficients j {A' (i) + A" (i)} and | A (2)
numerically, the required quantity x is
*» + - {a' (0 + A" (0} X r + - A(z) X T*.
2 2
This formula is very conveniently adopted to logarithmic com-
putation ; but is subject to the inconvenience of change of sign
in nearly every element.
The first step of improvement may be made by referring
the time for computation, not to the second ephemeridal time
Tj, but to the first ephemeridnl time T,. Thus, while we
always adopt, for the middle ephemeridal time T^, that ephe-
meridal time which is nearest to the time for which the inter-
polation is to be made, let us refer the interpolation time to
T, ; or, let us call the interpolation time T^ 4- 1. The value of
t (estimated in the same manner as that of t) will always be
included between 4- J and 4- f , and wiU, therefore, be essen-
tially positive. The formulas of interpolation will now be
«• = *, + {a'(i) — - a (2)} X / + i A (2) X <*.
The factors t and t^ are now positive ; but the coefficients
A' (i) and A (2), as before, still present in an unusual degree
the practical troubles attending changes of sign ; they are
formed sometimes by subtracting a lower number from an
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238 Astronomer' Royal, on a Method of
upper ; sometimes the difference has the same sign as the
number differenced, and sometimes a different sign ; and there
are the usual troubles attending the signs of the coefficients in
the interpolation-formula, and the aggregation of the terms.
In order to remove all the troubles attending the differ-
ences, an examination was made of the elements for which we
have usually to interpolate. Those subject to the greatest
changes are the Moon's R.A. (in seconds of time, and given
for every hour), the Moon's N.P.D. (in seconds of arc, and
given for every hour), and the Moon's Parallax and Semi-
diameter (in seconds of arc, and given for every twelve hours).
(The first difference of the Moon's R.A. is never negative;
but, for uniformity of system, it was included under the same
form of calculation as the others.) On examination, it was
found that for N.P.D. the greatest negative first difference
never amounted to — 20', and the greatest negative second
difference never to — i ; that for Parallax and Semidiameter,
the greatest negative first difference never amounted to — 40",
and the greatest negative second difference never amounted to
— 10"; and that for R.A, the greatest negative second differ-
ence never amounted to — i o*. Therefore, if we prepare the
following quantities (which, in a proper skeleton form, is a
very simple process, and involves no change of sign and no
subtraction): —
For Moon's Parallax
For Moon's R.A. For Moon's N.P.D. and Semidiameter.
d?, *i »i
a?a + 40* d?j + 20' d?3 + 40"
j?3 + 90* iPg + 41' d?3 + 90";
and if we then take their first and second differences, every
operation of forming differences is a subtraction of an upper
number from a lower ; every number so formed is positive ; the
coefficient A' (i) — J A (2) is always formed in the same man-
ner; every number to be substituted in the last formula of
interpolation
X, +{A'(l)-iA(a)} yi + ^ A (2) x <«
is positive ; and every operation of connexion of results is a
numerical addition.
But, in this process, we have introduced into our final sum
a quantity which depends upon our additive numbers (40 and
90, or 20 and 41), which quantity must now be subtracted.
Taking the differences of these numbers.
40
40
90
50
o
20
41
20
21
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Computing Interpolations Sfc.
239
it will be seen that we have introduced the quantity
o+35x/ + 5xf»
o + — x/ + I X i^.
7. 2
Tables of these quantities (called Table T* and Table T**)
are computed with the argument t ; and, from one of these
tables, T* or T** is taken (according to the series of additive
constants which has been used) and is applied, in all cases
subtractively, to the number produced by the interpolation-
formula.
It will be remarked that the numbers added for R.A. are
the same numerically (though in different denominations) as
those for Parallax and Semidiameter, and, therefore, the same
table T* is applicable to those three quantities. But the
tabular intervals are different, being i** for the R.A. and 1 2^ for
the Parallax and Semidiameter. This requires a modification
of the arguments. The first and last numbers of Table T* are
as follows: —
For
R.A.
For Parallax
. and Setnid.
t:
For
R.A.
For Parallax
and Semid.
T».
m 8
30
h
VI.
m B
18-750
m
89
B
55
h
XVII.
m 8
59 'o
63-681
I
11
18*761
56
12
63-695
z
24
18771
57
24
63-70^
3
36
18-783
58
36
63-722
4
48
18-794
59
48
63-736
5
I
i8'8o6
90
XVIII.
63-750
For T**, which is used for North Polar Distance only, a
single column of arguments suffices. The first and last
numbers of Table T** are as follows: —
i.
,
t
For N.P.D.
T**.
For N.P.D.
T**.
m 8
m
8
30
9 52-500
89
55
30 20-750
I
9 51-833
56
30 21-000
2
9 53"i67
57
30 21-450
3
9 53'5oo
58
30 a I -800
4
9 53-833
59
30 22-150
5
9 54-167
90
30 22-500
This system of interpolation has now been exclusively used
at the Royal Observatory from the beginning of 1862.
Royal Observatory f Greenwich,
1866, March 27.
Digiti
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240 M. Goldschmidty the New Star of the Year ^g^ A.C.
The New Star of the Year 393 A C: Documents taken from
the Chinese Observations of Ma-tuan-lin, translated by
Edouard Biot^ and the Remarks of M, Humboldt in his
Cosmos.
{Communicated by M, Hermann Goldschmidt,)
It is a long time since I attempted to prove that the new
stars of the years 393, 827, 1203, and 1609, are one and the
same. I was struck by the fact that the three first stars were
seen in the same constellation o£ Scorpii. That of 393 was
visible in the month of March near the star ft,^. The new star
of the year 1 203 was exactly on the same place of the sky at
the end of July.
The interval of time between these two apparitions are 8x0
years and a few months, and the half of this is 405 years and 70
days. If this epoch represents the duration of a period, the star
should have come back in the year 798. The Arabic astro-
nomers mentioned a new star on the 1 5th degree of Scorpii, in
the year 827, but the date is given as doubtful. It is said that
in the year 827, this star was observed under the reign of the
Calife Al-Mamoun, who governed between the years 814-833.
On taking for exact a period of 405 years, the star should have
returned again to its visibility at the end of the year 1 608, or
at the beginning of 1609; and, indeed, M. Biot found men-
tioned a brilliant star in the year 1609, in the Chinese col-
lection of Ma-tuan-lin. The historian only says that the star
was seen on the south-west of the firmament, but it is essential
that a new star appeared in that year. New stars ar j not so
frequent as to exclude this apparition, which is ranging itself
with the period of 405 years.
These considerations are sufficient, I think, to show the
probability of a period. The year 827 is alone given as
doubtful by M. de Humboldt in his Cosmos, remarking that the
apparition is to be put rather in the first half of the ninth cen-
tury ; but we learn that the star, was observed by the cele-
brated Babylonian astronomers, Hali and Giafar Ben-Moham-
med Alboumazar, under the rcdgn of the Calife Al-Mamoun.
This prince was himself' an astronomer, and this science flou-
rished under his reign. Considering these facts, the year of
the apparition cannot be so doubtful as to give a latitude of
half a century.
The anomaly of this star, which was seen in the year 827,
I suppose, instead of 798, or twenty-nine years later, cannot
raise any serious doubt of its identity with the other ones.
Can we not find any analogy with some variable star ? I have
observed U Geminorum (Hind No. 6) coming exceptionally
back 24 days before its ordinary return, and this with a period
of 96 days. It remains scarcely 1 2 days visible, and the
greatest light is for 2-3 days duration. The apparition of
Digiti
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Mr. Talmagty Observation o/Biela's Comet. 241
29 years later for the new star, can also be regarded as an
irregularity exceptional, for the other apparitions concord with
the period assigned, and it is not probable that the star of
1609 was another one. For U Geminorum we count days of
its irregularity, and for the new star of 827, years. We have
then
I. Apparition of the year 393 March.
* 798
827
3* ••• ••- 1203 End of July.
4. ... ... 1609
5. Reapparition probable 20 14-20 15
It is remarkable that 134 years b.c. a new star was seen in
ScorpiuSy which it is believed gave to Hipparchus the idea of
laying down a catalc^ue of stars. In CMna there was also
seen in the year 1 584 a star near 9r Scorpii.
FmtamebleaUf March 2, 1866.
On a Probable Observation of Biela*s Comet.
By C. G. Talmage, Esq.
In communicating .this observation to the Society, it is, I
think, necessary to enter somewhat into particulars. At our
last meeting I was publicly asked whether I could give any
information respecting Biela's Comet. I then stated that I
could not positively give an observation, but that, while sweep-
ing for Biela's Comet, on the 4th of November last, I came
upon a nebulous object that I think is very likely to have been
the Comet, and I here give extracts from my letters to my
friend Mr. Hind on the subject.
** 1865, November 9.
"... On the 4th, between a break in the clouds, I got a
glimpse of a cometic-looking object, the instrumental position
of which was
h m •
R.A 22 55 4
^ ,. . o , ,
Declination ... + 13 25 55
h m •
Local Sid. Time ... » o 20 12*07
Clouds closed up so quickly that I could obtain no comparison
B 2
Digiti
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242 Mr, Talmage^ Observation of Biela's Comet.
with any star ; it was exceedingly faint ; every night since
has been exceedingly dark/'
** 1865, Nov. 17.
" I have been waiting to get a sight of my object of the
4th, but we have had dreadful weather, not a star visible all
night.
'* These are the first observations since the return of our
hour-circle (hours given below)."
From Mr. Hind to myself :
** Richmond, 1865, Nov,zo.
" Pray look with all your eyes for Biela. I think in all
probability your object of the 4th was really nucleus L. Mr.
Barber caught a glimpse on the 18th of a cometary object
nearly on the declination of my ephemeris for Jan. 27*66, and
following something less than a minute. I expect this is about
the most likely position for it to turn up."
I may also give an extract from a letter of Mr. Hind,
dated 1 865, Nov. 8, which crossed mine in the post :
" On Sunday I had a close search here, and certainly sus-
pected a nebulosity not far from the place with P.P. Jan. 27, but
could not decide about it ; only clear for twenty minutes."
An exact copy from my observing-book :
1865, November
4.
Hour Circle
h m B
13 25 8 .-.
h m B
125 8 W.
Declination Circle...
/ //
+ 13 25 55
Corrected for refraction.
Sidereal Time
h m s
20 30
B
Clock Error = + 17*93.
G.M. Time
.-.at
9 23 42-30
20 12*07
h m B
R.A. = 22 55 4-07
Dec. = +13 25 55
On the 1 6th, the first fine night after the 4th, the index-
errors were determined by « Pegasi and ^ Pegasi to be
8
Error of Hour-circle by a, Pegasi = + 18*53
,, ,» ? Pegasi - + 18*67
8
Adopted Error <= + i8*6o.
And the Adopted Error of the Declination Circle = — 2"* 6
which reduces the observation to
Leyton
Declination
Sidereal Time.
R.A. of Object.
of Object.
G.M.T.
h m 8
h m B
/ *
h m 8
20 12*07
2a 54 45-47
+ 13 26 21
9 n 4^-30
Digiti
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Mr, Knotty on the Companion to Sirius. 243
Compared with Mr. Hind's Ephemeris, with P.P. of Jan.
27-66, the errors are
A » = — 26*07 A J « — I 2
Mr, Barclay* 8 Observatory, Leyton,
Occultaiion of ^i Arietis, 1866, March 19.
By C. G. Talmage, Esq.
h m ■
G.M.T. of disappearance = 7 54 25*26
,, reappearance » 8 15 30*79
At the disappearance on the dark limb, the star was pro-
jected on the Moon's disk for a very appreciable time ; the
limb of the Moon being distinctly visible on the following side
of the star. The reappearance is considered good, several
small stars were occulted during the time the star (3 1 Arietis)
was hidden by the Mooni .
Power 80 on the 10 -inch refractor.
On the Companion to Sirius, By Greorge Knott, Esq.
Happening to turn my 7J-inch Alvan Clarke refractor on
Sirius f on the 24th of January, I was surprised to find the
small companion, notwithstanding bright moonlight, a tolerably
conspicuous object. Its colour was a fine pale blue (about
Blue' of the late Admiral Smyth's chromatic scale), and it bore
a sufficiently strong illumination to allow of my measuring it
in position and distance with a wire-micrometer, mag. power
375, with the following results : —
P ■■ 77°*2i ob«. 5, w. 22; D = io"*433 obs. 4, w. 10; Epoch 1866*064.
On the 2nd of February, although the atmosphere was too
disturbed to allow of distance-measures being taken, I again
succeeded in measuring with the wire-micrometer and power
275, the angle of position of the companion as follows : —
P s 77^*04 obs. 5, w. 10 ; D impossible ; Epoch x866*o88.
Combining the two sets, allowing weights, we have the follow-
ing mean results : —
P » 77°* 1 6 obs. 10, w. 32 ; D = io"'433 obs.4> w. 10; Epoch 1866-07.
Digitized by VjOOQIC
244 ^^'"'^ CoUanty Companion of Antares.
Of course, in the case of a pair so difficult to measure,
especially in these latitudes, these results are open to some un-
certainty, but they will be found to present a fair accordance
with the predictions of Dr. Auwers' Ephemeris, printed in the
Monthly Notices for December 1 864, the calculated co-ordi-
nates for i866'o being P=78°*5o, D=io"75. I do not
know that much importance is to be attached to the circum-
stance, but it may perhaps be worthy of a passing remark that,
with the single exception of the measures of the Rev. W. R.
Dawes in 1864, all the observed angles of position quoted by
D. Auwers (and my own result may now be added to the list)
are less than the calculated angles.
I had hoped to have succeeded in obtaining further mea-
sures of this interesting pair, but have hitherto been prevented
from doing so by unfavourable weather. I may just remark,
in conclusion, that my measures on February 2 were taken with
the aperture of the telescope reduced to 6^ inches, and that on
that occasion I found that the small star was still visible by
glimpses with 5 inches of aperture, and I am quite inclined to
indorse the opinion expressed by Mr. Dawes that the visibility
of the small star is dependent rather on the Condition of the
atmosphere than on the size of the telescope.
Woodcroft Observatory, Cuckfield,
April IX, 1866.
Companion of Antares. By Arthur Cottam, Esq. F.R.A.S.
With reference to the last part of Mr. Freeman's note in
the last Monthly Notice, I may mention that on two evenings
at the end of last summer I saw the Companion without any
difficulty with a 4 J -inch object-glass. I have not since been able
to observe Antares, but, on both the evenings referred to, the
Companion was at times clearly separated from the blaze of the
large star, and certainly appeared to be of a green colour. On
the second evening my brother, who happened to be with me,
saw the Companion also. On both occasions the star was at
least an hour west of the meridian, and the atmosphere not
particularly good. The powers used were 150 and 200.
My Observatory here stands at an elevation of 500 feet
above the sea level, and it is very rarely that I am prevented
by fog from making observations.
As I supposed that a 4|-inch object-glass ought to show
the companion of Antares, I have not before diought this
worth communicating to the Society, but after seeing Mr.
Freeman's note I am inclined to think that my position must
be a good one.
Bushey Heath, Watford, Herts,
April 12, 1866.
Digiti
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245
On a Small Star near $ Cants Majoris,
By D. A. Freeman, Esq.
I beg leave to state that I have observed a small star near
to i Cants Majoris, It is «, a little /• On comparing its dis-
tance from f with the distance between Bigel and its Com-
panion, I estimate that its distance is rather less than the latter,
and .that its magnitude is 1 2 or 13. Owing to the low altitude
of f, the small star is difficult to observe with my aperture of
4|-inch, and I did not feel quite certain of its existence until
yesterday evening, when the very fine atmosphere, which
enabled me to see the 5th and 6th stars in the trapezium with
equal facility, dispelled all doubt about it.
I am not aware whether this small star has been the sub-
ject of observation, and its position and distance measured.
There are other minute and faint stars at a greater distance,
n,p. the large star.
Mentone, Alpet Maritimei,
%l March f 1866.
The French Academy of Sciences have awarded the La»
lande Prize for Astronomy to Mr. Warren De La Rue, for his
Works in Celestial Photography. The Report of the Com-
mission, consisting of MM. Mathieu, Delaunay, Liouville, Faye,
and Laugier, drawn up by M. Laugier, and published in the
Comptes Rendus, March 5, 1866, is as follows: —
" n y a bientot vingt-sept ans que la decouverte de Da-
gaerre est connue, admiree et exploitee dans le monde entier.
Grace a an grand nombre de travaux distingues, dimportants
perfectionnements ont et6 realises, et celle belle invention a fini
par donner naissance en quelque sorte k une nouvelle branche
d'industrie. Les sciences d*observation, TAstronomie entre
autres, n'ont pas tard^ k lui devoir de notables progr^s. Nous
n'entreprendrons pas d'exposer dans ce Rapport les titres des
astronomes et des physiciens qui ont contribu^ k ces progr^s :
seulement nous aliens faire connaitre en quelques mots ceux
qui ont signale Tun d*eux, M. Warren De La Rue, au choix de
la commission du prix Lalande.
" H y a dixhuit ans que M. Warren De La Rue a £tabli son
observatoire priv6 k Cranford, pr^s de Londres, et depuis
qainze ans environ il s'est specialement livr^ a I'etude de la
photographie celeste. L'instrument qu'il a employe dans ses
laborieuses et delicates recherches est un telescope de 1 3 pouces
anglais d'ouverture, mont6 sur un pied parallactique mti par
une horloge et construit sous sa direction d'apr^s ses dessins.
Les belles photographies lunaires que M. De La Rue a fait
connaitre au monde savant prouvent le degre de perfection de
Digiti
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246
son grand appareil sous le double rapport optique et mecanique.
A I'aide du mecanisme d'horlogerie.il pent modifier le mouve-
ment de sa lunette et lui faire suivre exactement les variations
de la Vitesse de la Lune. En perfectionnant les procedes chi-
miques employes pour la preparation de la surface sensible, il
est parvenu a reduire notablement la dur^ d'exposition de
cette surface k Taction des rayons lumineux. Enfin tour a
tour opticieu, m^anicien, chimiste, et astrouome, M. De La
Rue a eu la satisfaction de voir ses efforts couronnes de succ^.
Les images photographiques de la Lune qu'il a obtenues a
diverse reprises sont d'une perfection telle qu'elles peuvent
supporter Tamplification considerable de 36 pouces anglais en
diam^tre : et elles se pretent a des mesures microm^triques si
exactes qu'elles ont fourni des donnees precises pour la mesure
de la libration.
*<Dans les stances memorables de TAcad^mie des Sciences
oil Arago rendit compte des procedes de Daguerre, il 6nu-
merait les applications que I'Astronomie pourrait en faire un
jour, et dej4, d'apres la premiere ^preuve de la Lune que
Daguerre avait obtenue sur sa demande, il predisait qu'on
ferait des chartes photographiees de notre satellite. Cette
prevision se realise en ce moment : les belles ^preuves de M.
De La Rue sont employees comme fondements de la grande
earte de la Lune de 6 pieds anglais de diametre, entreprise sous
les auspices et d'apres les ordres de T Association Britanique
pour Tavancement des sciences. II est parvenu a produire des
vues stereoscopique lunaires qui peuvent faire connaitre exacte-
ment les hauteurs et les depressions relatives des ravins, pla-
teaux, et ondulations dont la surface de la Lune parait sillonee.
Ajoutons que M. De La Rue a ^galement obtenu des epreuves
photographiques de Saturne, de JupiteVy de Mars^ et de
quelques etoiles.
" Ces beaux travaux de photographie celeste sugger^rent en
Angleterre Tidfe d'^tablir a TObservatoire de Kew un instru-
ment special, et ce fut naturellement k M. De La Rue qu'on en
confia la direction. Depuis 1858 qu'il est installe, Tappareil
hMiographique de Kew a donn^ plusieurs resultats importants.
Lors de r^clipse totale du Soleil en i860 il fut emporte en
Espagne par M. De La Rue k la demande de la Soci^te Royale
Astronomique, et cette habile astronome put prendre une s^rie
d'^preuves de Teclipse, avant, pendant, et apres disparition totale
du Soleil. Des mesures effectuees sur ces Epreuves k Taide
d'un micrometre invente par M. De La Rue furent soumises
au calcul, et la discussion montra que les changements angulaires
des preeminences lumineuses par rapport a la Lune s'accordent
avec Thypoth^e de leur adherence au Soleil ; que I'apparence
des flammes ne varie qu'en raison du deplacement de la Lune,
et ne soubit aucune autre alteration ; de sorte que lorsque le
^ mecauisme d'horlogerie est ajuste sur le mouvement du Soleil,
les flammes paraissent immobiles. Enfin la comparaison des
Digiti
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247
photographies de I'^clipse obtenues k Bivabellosa, ou observait
M. De La Rue, avec celles que le P. Secchi obtint au Desierto
de las Palmas, montra I'identit^ des preeminences observ^es
aux deux stations, en tenant compte bien entendu des efibts
de la parallaxe dus k la difference des stations ; etablissant
ainsi qu'aucune modification des preeminences pendant un laps
de temps beaucoup plus long que la duree de Feclipse totale,
puisque, dans ces deux stations, le ph^nomene se produisit a un
intervalle de sept minutes.
"En 1859 ^' I^e La Rue obtint des vues stereoscopiques
du Soleil, en profitant de son mouvement de rotation sur son
axe, et ces vues de taches et de facules permettent d'etudier les
positions relatives des parties qui composent la photosphere.
II a montre ^galement la possibility d'obtenir par Taction de la
lumi^re seule, des plaques pouvant imprimer avec les encres
ordin aires d'imprimerie les epreuves photographiques de la
Lune et du. Soleil.
"Depuis 1863 I'appareil h^liographique de TObservatoire de
Kew fonctionne sans interruption, et les Epreuves quotidiennes
sont relevees et discut^es sous la direction de M. De La Rue.
Enfin sur la demande de la Gouvernement Russe un second
appareil du meme genre a ^te ^tabli k Wilna, et le directeur de
cet observatoire a re9U de M. De La Rue toutes les instructions
n^cessaires pour en faire usage.
" Conclusions.
" La Commission propose a FAcademie d'accorder k M.
Warren De La Rue, pour I'ensemble de ses beaux travaux de
photographie celeste, le prix d' Astronomic de la fondation
Lalande."
Instrument for Sale.
To be disposed of, a 3 2 -inch Transit Instrument, made by
Simms, London, mounted on stone pillars; 2 J -inch object-
glass; declination and micrometer circles, divided on silver
collimator; three eye-pieces, 37, 66, 100; prism for zenith
observations; stride level, &c. &c. For further particulars
inquire of J. Jenkins, Esq., Rotherslade, near Swansea.
With this Number are issued plates to illustrate Mr. Hew-
lett's paper on Sun-spots, printed in the first number of the
present volume, p. 13.
Digiti
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248
CONTENTS.
Page
Fellows elected 221
On the Supposed Possible Effect of Friction in the Tides, in influencing
the Apparent Acceleration of the Moon's Mean Motion in Longi-
tude, by the Astronomer Royal ib.
On a Method of Computing Interpolationa to the Second Order without
Changes of Algebraic Signs, by the Astronomer Eoyal . . . . 246
The New Star of the Year 393 a.c: Documents taken from the Chinese
Observations of Ma^tuan-lin, translated by Edouard Biot, and the
Remarks of M. Humboldt in his Oosmotf by M. Goldscbmidt . . 240
On a Probable Observation of Biela's Comet, by Mr. Talmage . . 241
Oocultation of 3 1 Arietta, 1866, March 19, by Mr. Talmage . . . . 243
On the Companion to Sirius, by Mr. Knott ib.
Companion of Antarea, by Mr. Cottam . . . . . , 244
On a Small Star near 1 CanU Mqforig, by Mr. Freeman . . . . 245
Award by the French Academy of Sciences of the Lalande Prize to Mr.
Warren De La Rue ib.
Instrument for Sale 247
Printed by Stbamobwats and Waldbh, Caatle St. Leicester Elq. and PttblishCRl
at the Apartments of the Society, Ifay ti, 1866.
Digiti
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University c.
MONTHLY NOTICES
OF THB
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVL May ii, 1866. No. 7.
Warren De La Rue, Esq., Vice-President, in the Chair.
Henry Boys, Esq., Cambridge ;
Samuel Hunter, Esq., Kingstown, Ireland ;
Josiah Thomas Slugg, Esq., Manchester;
Edward Carlton Tuffnel, Esq., 26 Lowndes Square ;
Rev. H. Storer Toms, Enfield ;
Williams Nutter Barker, Esq., Enfield ;
John Smith, Esq., Dorking ; and
J. E. Saunders, Esq., 9 Finsbury Circus,
were balloted for and duly elected Fellows of the Society.
Dr. Auwers, Gotha ;
M. Hermann Goldschmidt, Paris ;
Dr. Forster, Berlin ; and
Lieutenant SafiTord, Chicago,
were balloted for and duly elected Associates of the Society.
TUe Semidiameter of the Moon according to M. Hansen^s
Tables of the Moon, compared with the results of the
best Observations, By J. A. C. Oudemans,
{Translated Jrom a trantlaiion into French communicated by M, Hoek,)
Though complaints are made of the uncertainty of the
planetary diameters, as obtained from micrometric measure-
Digiti
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250 Jf. Oudemans, Semidiameter of the Moon
ments, yet the diameter of the Moon is no better known to us.
In 1 85 1, 53, 54, and 58, M. U. De Lange and I have observed
many occultations of the stars, which I have used to calculate
the longitude of Batavia. The observations indicate clearly
that the semidiameter of the Moon, as given by the Tables of
M. Hansen, has need of a negative correction. To control this
indication, I have brought together all the determinations
known to me of the aforesaid element by means of total and
annular eclipses, of occultations of stars, and of measurements
made by the aid of a heliometer. I remark, first of all,
that M. Hansen has adopted the arithmetical mean which
the meridian instruments at Greenwich have given for the
two diameters of the Moon, horizontal and vertical. Then,
whatever errors there were in the expressions according to
which Burckhardthas calculated his Tables of Lunar Parallax,
these errors have an influence on the semidiameters deduced
from observations at different periods. The most part of the
calculations that I have employed give the correction of the
semidiameter of Burckhardt's Tables. It was necessary then to
reduce them to M. Hansen's Tables. I have done this by means
of Mr. Adams' Tables {Nautical Almanac^ 1856). The follow-
ing are the details of ray results : —
A. Occultations of the stars by the Moon.
I. Occultations of the Pleiades^ 29th Aug. 1 820, calculated
by Rosenberger {Konigsherger Beohachtungen IX Abtheilung^
p. v.).
As the observation of this phenomenon had succeeded very
well at Konigsberg, and the positions of the stars were exactly
known, Rosenberger has deduced from it the correction of the
semidiameter of the Moon. Four immersions combined with
six emersions give him
Correction of Burckhardt's Semidiameter . , . . « + 0*07
I find :—
Reduction of Burckhardt's Tables to those of Hansen . . « — 0*93
Correction of Hansen's Semidiameter . . = _ o*86
2. Occultation of tf' Tauri, 28th March, 1830, which M.
Kaiser has used for the determination of the longitude of the
Observatory of Leyden (Memoirs of the R. A, S., vol. x.
p. 303)- .
The immersions as well as the emersions were observed at
Leyden, Dorpat, and Mannheim. The final equation —
Corr. of the Semidiameter = 2"*94 — 0*0023 ^{fi — b) + 0*0004 ^ «-,
Digiti
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(iccording to M. Hansen^ s Tables of the Moon, 251
is perfectly applicable to our purpose. It will be sufficient to
consider as zero the two quantities ^ (/3 — 6) and } t, which at
most are not more than some seconds : whence^
Correction of Burckhardt's Semidiameter . . + 2*94
But we have :
Reduction of Burckhardt's Tables to those of Hansen — 3*43
CorrectMMi of Hansen's Seaiidiameter . . — 0*49
3. Occultation of a Tauri^ loth February, 1832, also
employed by M. Kaiser.
The complete observation was successful at Mannheim,
Cambridge, Aberdeen, and Greenwich. The equations give :
Correction of the Semidiameter « + o«"33 — 0*055 >«*.
I find:
)«* » Parallax according to Adams — that according to
Burckhardt . . . . « - o"-46
Then:
Correction of Burckhardt's Semidiameter . . . . = + 0*36
Reduction to Hansen's Tables — i'47
Correction of Hansen's Semidiameter .. — - i*ii
4. Occultation of the Pleiades loth Aug., 1841, calculated
by Lejeune (Dmertofto AstronomuB Inauguralis, Lugd. Batav.,
1845).
An excellent determination resting on a great number of
observations. Fifty-two equations combined according to the
method of least squares, gave : ^/ = -f i"'33 — 0*259 )«• w^*^
a probable error ± o"'og ; here ^/ = «■)«, where «• is the
parallax, k the ratio (o 2725) of the sine of the semidiameter
to the sine of the equatorial horizontal parallax. The cor-
rection of the semidiameter is therefore —
«•>» + X ?ir = )/ + 0*2725 2sr
■■ i"'33 + 0-0135 Jw.
I find—
)«*, or the parallax according to Adams — that ac-
cording to Burckhardt . . . . «• + 3"'44
whence it follows, —
Digiti
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252 M. OudemanSy Semidiameier of the Moon
m
Correction of Burckhardt's Semidiameter -1-1*83
Reduction to Hansen's Tables . . . . — 2*49
Correction of Hansen's Semidiameter .. — i*ii
B. Total Eclipses of the Sun.
I. The Eclipse of July 7, 1842. M. Olufsen's calculations
(Astron, Nach. xxii. p. 217) gave him, —
ir ^ » » — i*"os — 0*296 ) «•
add to this —
» J«r = 0*2725 )«*
and we shall have :
Correction of Barckhardt's Semidiameter » — 2*^^05 — 0023 5 ^<r.
Mr. Adams' Tables (iVawft'ca/ -^/wawac, 1856) give for this
date ^;r = — o"*4, therefore
Correction of Burckhardt's Semidiameter . . ■■ — 2*04
Reduction to Hansen's Tables . . . • «■ — 1*46
Correction of Hansen's Semidiameter .. .. ■.—3-50
The same eclipse has been calculated by Carlini. Unfor-
tunately I could not at Batavia consult his Memoir, which is
in the Giornale delV Instituto Lombardo, vol. iv.
M. Santini has quoted the results in his account of the
eclipse of July 28, 1851, these results differ very much from
those of M. Olufsen : " H semidiametro lunare," says Santini,
'' poi corrispondente alia parallasse equatoriale di 60' fu dal
Signer Carlini assegnato = 16' 2o"*4."
Burckhardt's Tables give for this date a parallax of
59' 5 8"- 8. The discussion of the observations by Carlini has
therefore given a semidiameter during the eclipse of 16' 20" 07,
while Burckhardt's Tables give 16' 2o"7.
The result is :
Correction of Burckhardt's Semidiameter . . — 0*63
Reduction to Hansen's Tables ,. .. — 1*46
Correction of Hansen's Semidiameter
;*o9
2. The total Eclipse of July 28, 1 851, of which there are
a great number of observations, but which have not yet been
completely discussed. Santini submits the observations of ten
observatories to calculation, and has deduced from thence the
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according to M, HanserCs Tables of the Moon. 253
corrections of latitude and longitude of the Lunar Tables {AsU
Nach. xxxiv. p. 289).
The observations at Dantzig have been employed there in
the determination of the longitude of that place.
The f6ur phases observed at Dantzig, when the erroneous
^quantity in the 12th equation -f 5"'36 is replaced by — 5"*36,
give:
Correction of the Semidiameter of the Sun . . — 0*65
,, „ Moon (Burckhardt) —0*75
while the observations at Konigsberg where the eclipse was
also total, gave to Santini :
Correction of the Semidiameter of the Sun . . — 3*07
,, ,, Moon (Burckhardt) — 07b
The first of these two last quantities attains a value, im-
probable because of its magnitude, and incompatible with the
results of the observations at Dantzig. The second, for this
reason, deserves little confidence. But, fortunately, we have
the researches of Wichmann, who introduces into his calcu-
lations the measurements of the distance of the horns {Ast.
Nach, xxziii. p. 309), and who obtains :
Correction of Burckhardt's Semidiameter of the Moon — o"79
which agrees well enough with the result of the Dantzig
observations.
We have, then, for the date of this eclipse : —
ParaUax according to Burckhardt {Naut, Aim,) = 60 30*2
Correction according to Adams {Naut, Aim.) = —0*3
Parallax according to Hansen ^i 60 29*9
Semidiameter corresponding to this Parallax := 16 30*75
Semidiameter according to Burckhardt (Memoir by Santini) ^ 16 29*2
Correction of Burckhardt's Semidiameter . . » ^0*75
Reduction to Hansen's Tables ~ i*55
Correction of Hansen's Semidiameter .. ■« —2*30
C. Annular Eclipses of the Sun.
I. The annular Eclipse of the 7th September, 1 820, of which
the observations have been calculated by several astronomers,
Walbeck, Santini, RUmker, Wurm, and Biirg.
Walbeck has determined the moment of the conjunction
according to the observations of seven observatories. Those
of Gottingen, Cuxhaven, Bremen, and Mannheim, places where
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254 ^' Oudemans, Semidiameter of the Moon
the eclipse was annular, gave him, for the correction of the
semidiameter, according to Barckhardt's Tables, the following
quantities: —
The obtcnrati
ons of Gauss
+ 2-73
Harding
+ 3*79
Strove
■|-a'»o
Walbeck
+ 2-02
Olbers
■♦•ro6
,, Gildemeister
+ 0*85
TraUes
+ 0'I0
Nicolai
+ 1-66
, Heiligenstein
+ I'2I
Mean -♦• 1*74
I have combined the results of Walbeck's calculations in
another manner.
The four astronomers whose names occur first in the pre-
ceding table, all observed at Gottingen ; Olbers and Gilde-
meister at Bremen ; Nicolai and Heiligenstein at Mannheim.
Now it is clear that the local irregularities of the limb of the
Moon have influenced alike all the observations in one place.
I have, therefore, preferred the following combination : —
Mean of the observations at Gottingen + 2*68
«, t, Bremen + ^'95
,, ,, Coxhaven -t-o'io
,, ff Mannheim + 1*44
Mean +1*29
The semidiameter of the Moon, having been adopted bj
Walbeck =88 1 "'02 (Correspofulance Astronomigueyiv, p. 501),
we have, according to these calculations : —
Semidiameter of the Moon according to the observations of the
Eclipse of the 7th September, 1820 .. . . 882''' 31
The calculations of Santini are mentioned at the same time
as those of Walbeck in the report by Von Zach. " M. San-
tini," he says, "has also calculated a very great number of
observations of this eclipse ; he is working at a memoir, which
he is going to publish shortly. In the meantime, these are
some of the results which he has communicated to us : —
Correction of Burckhardt's Semidiameter of the Moon + 1"*39
I, therefore, admit here the same value of the semidiameter
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according to M, Hansen's Tables of the Moon, 255
as in Walbeck's calculations. On this supposition Santini's
calculations lead to the result : —
Semidiameter of the Moon, 7th September, 1820 = 882''*4i
Biimker's calculations (Berliner Astronomisches Jahrbuch^
1824, p. 153) embrace the observations made at 18 places.
Among them are Amsterdam, Bergen, and Zurich, where
the eclipse was annular, and also the four places already men-
tioned on the occasion of Walbeck's calculations. Riimker
adopted —
Semidiameter of the Moon a 881*0
and he found
Correction . . =* + o* 14
True Semidiameter » 881*14
Biirg's results rest on a total of 51 observations made
in twentj-one places (Berliner Astronomisches Jahrhuch^ 1 824,
Pt 119). The elements of his calculations deduced from his
own tables assume
Semidiameter of the Moon = 883*1
a quantity for which the observations indicate
Correction of «» - 2*3
from which it follows that
True Semidiameter ■= 880*8
Lastly, the Berliner Astronomisches Jahrhuch of 1825,
p. 89, contains Wurm's calculations. A total of 172 ob-
servations made at 79 places were compiled l^ this calculator.
Although he was obliged to reject many, particularly at the
commencement of the eclipse, he succeeded in basing his results
upon a number of observations far larger than that employed
by the other calculators. He finds —
•» «
Correction of the Semidiameter adopted — 2*1 8
Semidiameter adopted in the calculations 882*90
True Semidiameter of Sept. 7th, 1820 = 880*72
By means of Mr. Adams' Tables I find —
The Semidiameter according to Hansen's Tables « 883''' 3 5
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256 Jf. Oudemans, Semidiam^ter of the Moon
from whence it follows : —
Correction according to Walbeck » — 1*04
„ „ Santini «— 0*94
y, „ Riimker =»— 2*21
M Biirg =-2-5S
„ „ Wurm «-2*63
Of these results the last is most to be depended upon^ as it
is based upon the greatest number of observations.
2. The annular Eclipse of May 15th, 1836. Riimker's cal-
culations (Astr. Nachr, xiv. p. 97) give the expressions for
the moment of conjunction, but not the other results.
If we introduce, for the places whose observations em-
brace the commencement and the end of the eclipse, the condi-
tion that these two phenomena ought to give an equal value
for the moment of the conjunction, we obtain the relations be-
tween the sum of the corrections of the semidiameters of the Sun
and Moon as x, the difference of these two quantities = ^,
the correction of the latitude of the Moon = } /3, and the cor-
rection of the parallax of the Moon = ^9r.
The results of Biimker's memoir give me, according to the
method of least squares —
X — — i*i8 +o*io6 !«• «— 0*98 Weight « 72*11
y «— 0*69 +0*026 J «•=»— 0*64 „ 95'o6
2/3 ■•— 0*72 +0*586 J<r ^ +o'39 „ 8*62
seeing that we have for the difference of the parallax accord-
ing to Burckhardt and Adams
i«'= + i"-90.
But as Bumker had already admitted in his calculations
values
of ;p=-i"
„J^ — 7"-63
we have the following corrections of the data of the Nautical
Almanac employed by Bumker : —
Total * « — 1-98
Total y « - 264
Total J^ = - 7'24
of which the two first give —
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according to M, Hansen* s Tables of the Moon, 257
Correction of Borckhardt's Semidiameter of the Moon +0*33
Redaction to Hansen's Tables .. .. -1*97
Correction of Hansen's Semidiameter .. .. - 1*64
The observations of this eclipse do not agree with each
other ; I find the
Probable error of each observation
Therefore that oi a;
y
J/5.
I (« - y) «\/(o-a9)* + {P'zsf = 0-38
= 4*9
= 0-58
= 0-50
= 1-50
D. Measurements with a heliometer.
I and 2. Observations by Bessel of September 2, 1830, and of
December 26, 1833, dates of a total Eclipse of the Moon. Each
of Bessel's results is the mean of six diameters, taken at inter-
vals of 30^ of the angle of position. He finds,
2 Sept. 2i6Deo.
1830. 1833.
Correction of Burckhardt's Semidiameter . . 0*00 4- 0*73
But we have
Redaction to Hansen's Tables . . —1*42 —1*78
Reduction to Hansen's Semidiameter . . — 1*42 — 1*05
As to the difiTerence of these two results, Bessel himself
attributed them to the inaccuracy of the tables of the parallax
{Ast. Nach, xi. p. 410). But M. Hansen's more accurate
tables only reduce them one-half.
3. Measurements of Wichmann of July i, 1846 {Ast, Nach.
xxix. p. I). In this series of observations the measurements
follow at intervals of 5*^ of the angle of position. The observ-
ations were corrected for the refraction, according to the new
formulae. The phase was taken account of.
The measurements indicate that the Moon is not a sphere.
The differences between the measured diameter are as high as
2""48, a quantity which we cannot attribute to faulty observa-
tions. The mean gave.
Correction of Burckhardt's Semidiameter . . + 1*26
Reduction to Hansen's Tables . . . . - 2*66
Correction of Hansen's Semidiameter - i '40
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258 M, OudemanSj Semidiameter of the Moon
4. Measurements by M. Peters during the total Eclipse of
the Moon, of the 6th January, 1852, which were made under
such unfavourable circumstances that I thought it better to
reject the results. The eclipse began at 19^ 22™ mean time of
Konigsberg, while the Moon was at a height of 12^ above the
horizon, 38 minutes before sunrise. Peters himself said of
them, ^* Der Mond erschien um diese Zeit wegen seines niedri-
gen Standes hinter Diinsten des Horizonts und wegen der
eintretenden Morgendammerung so schlecht erleuchtet dass
ich nur die Schwachste Vergrosserung anwenden konnte. Mit
dieser sah ich indess das Nord-und Siid-rand deutlich " (Ast.
Nack, xxxi V. p. ii ). The result was,
Correction of Bnrckhardt's Semidiameter —
By 5 measurements in the angle of position 0° = — 'I'l
6 „ „ 90° - + 0-8
Mean — 0*15
Reduction to Hansen's Tables — 2*09
Corrections of Hansen's Semidiameter . . — 2*24
Summary.
Corrections of the semidiameter of the Moon deduced
from M. Hansen's Tables :
A. By occultations of Stars :
1. Occultation of the Pleiades, August 29, 1820 . . — o-86
2. ,, /Tauri, March 28, 1830 .. —0*49
3. „ » Tauri, February 10, 1832 — i*ii
4. 1, the Pleiades, August 10, 184 1 .. — i*ji
Mean
..
— 0-89
B. By total eclipses of the Sun :
I. Eclipse of July 7, 1842 \ O^^fsen
( Carlini
-3^50
-2-09
-^^80
2. y, July 28, 1851
..
-1-30
Mean .. .. .. — a'55
C. By annular eclipses of the Sun :
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according to M. Hansen's Tables of the Moon, 259
1. Eclipse of September 7, 1820 .. .. -2*63
2. „ May 15, 1836 .. -1-64
Mean
2*13
D. Bj measurements with a heliometer :
1. Measurements by Bessel, September 2, 1830 — 1*42
2. ,, ,, December 26, 1833 —1*05
3. ty ' Wichmann^ July 8, 1846 — 1*40
Mean — 1*29
As to these results, it is evident that the total eclipses of
the Sun point to a diameter smaller than that which the other
phenomena explain. In fact, the observations here give us the
disappearance and reappearance of the light of the Sun in the
gaps presented by the indentations of the limb of the Moon.
In the annular eclipses, on the contrary, we should find the
diameter at its maximum, if the observers noted the moment
when the limb of the Sun showed without any interception
by the mountains of the Moon. But there are other observers
who note the first and the last instant of the appearance and
of the disappearance of the series of luminous points, and it is
clear that their observations will give a minimum diameter. It
is to this difference of conception that Nicolai already attributed
the sensible difference between the observations of the same
eclipse and at the same place, but by different persons. It
therefore appears to me better to separate in the final result
the date furnished by eclipses, from those based upon occulta-
tions and direct measurements.
I obtain :
Correction of the Semidiameter in M. Hansen's Lunar Tables —
For the calculations of occultations .. -1*09
„ ,, eclipses . . . . — 2*34
Without doubt there are many memoirs on the determina-
tion of longitude by means of the occultations of stars which
would furnish us with ulterior data for the subject on which
we are engaged. It is true that there are a great number of
calculations which do not give the necessary differential equa-
tions. Wurm and Triesnecker have probably not even calculated
them. But there is in the Ast. Nach. a very great number of
calculations of longitudes. The index of the volumes i. to xx.
has 14 pages, each of 2 columns, of them ; that of vols. xxi.
to xl, 3 pages. Besides there are 3600 observations of occul-
tations which we find in the same journal, vol. i. to xlviii.
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zSo Mr. ffuggins, Observations on the
Lastlj, we must not forget the millions of analogous observa-
tions communicated in ^e Astronomisches Jahrbuch (1776-
1 830), the Allgemeine Geographische Ephemeriden (i 798-1 800),
the JMonatliche Correspondenz (1800-18 13), the Zeitschrift
fur Astronomie (1816-1818), the Correspondance Astronomic
que (18 1 8-1 8 26), — materials sufficient for an extended re-
search, which my occupations do not permit me even to
attempt. I shall content myself with having obtained a result
which is sufficient for practical purposes. For we must not
forget that the Moon is not a spherical body, and that the most
perfect acquaintance with its mean diameter will not enable us
to avoid small differences in the result of occultations.
For practice, then, I prefer to admit the following data : —
Relation of the diameter of the Moon to that of the Earth's
equator.
According to Hansen 0*272957
Correction corresponding / Ar = — i"*09 — 318
to .. .. ( . — 2*34 —684
Corrected relation . . |
0*27264
0*27227
Values of which that adopted by Burckhardt, 0*2725, is
about the mean.
Finally, as the mean equatoreal horizontal parallax is
56' 59"'57 according to M. Hansen, we have —
Semidiameter of the Moon :
According to occultations and direct measurements , „
by the heliometer . . 15 32*27
According to eclipses of the Sun . . 15 31*02
Bataoia, April 20, 1859.
Results of some Observations on the Bright Granules of the
Solar Surface^ with Remarks on the Nature of these
Bodies. By William Huggins, Esq., F.R.S.
I employ the word granules in preference to the other
names* which have been proposed for the bright particles of
* Stone calls them rice-grains; Nasmyth, willow-leaves; Dawes,
granulations and minute Jragments qf porcelain ; Chacomac, crystals ;
Brodie, shingle-beach. Sir W. Herschel's corrugations and bright nodules
may refer to the groups of granules and possibly sometimes to single granules.
Digiti
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Bright Granules of the Solar Surface. 261
the solar surface, because, as Mr. Dawes, who suggested this
term, well observes '* the appellation granulations or granules
assumes nothing either as to exact form or precise character."
In this paper I confine my remarks to the bright granules
as they appear on those parts of the Sun which are free from
the disturbing forces or currents which are active in the areas
of the spots. Under the influence of the forces by which the
spots are produced the bright granules assume different, and
with respect to their appearance on the general surface of the
Sun, irregular and unusual forms. In these regions of dis-
turbance the granules often appear to coalesce, sometimes to
be drawn out into very elongated forms, and occasionally to be
wholly dissipated within the umbra of a spot. On those parts
of the Sun however where the spots are absent these granules
appear to preserve, within not very wide limits, considerable
general definiteness of form, of size, and of mode of grouping.
It is to these normal characters only of the bright granules
that the observations of the present paper refer.
In a note I give references to the more important observa-
tions of others of these interesting bodies.*
Distribution. — With the exception, mentioned already, of
the areas containing spots, the bright granules are to be seen
over the whole surface of the Sun. Occasionally, granules pre-
serving their normal characters may be detected in the penum-
brsB and the umbras of spots. On one occasion, May 4, 1 866, I
resolved a large facula near the edge of the Sun's disk into an
aggregation of similar particles. Without the border of the
facula were two or three isolated granules of equal brightness
with those composing the facula. These granules appeared
as if they had become detached from the group forming the
facula.
Form. — When the granules are observed with powers of
about 100 diameters, no comparison which has been made
appears to me so appropriate as that to " rice-grains,** sug-
gested by Mr. Stone. If, however, higher powers are em-
ployed, this apparent regularity of figure and of size of the
granules disappears to a great extent. Many of them are then
seen to be nearly round, and not of the elongated form of rice-
grains. Besides the oval and nearly round granules, may be
observed irregular-shaped masses of almost every form. An
important character common to all these bodies, whatever their
* Dawes, Monthly NoiiceSf vol. xxiv. p. 140 and p. i6i; Nasmyth,
ibid. Yol. xxiv. p. 66; Stone, ibid. vol. xxiv. p. 124; Lockyer, ibid. vol.
XXV. p. 237 ; Brodie, ibid. vol. xxv. 233 ; Fletcher, ibid, vol. xxv. p. 231 ;
Huggins, vol. xxiv. p. 141; De La Rue,3femofV« Royal Ast. jS'oc. vol. xxziii.;
Chacornac, Reader ^ Jan. 7, 1865. See also for the interpretation of these
bodies, Faye, Comptes Rendus, torn. Ix. p. 13 S and p. 468 ; Brayley, Knight's
Companion to the AlmanaCy 1864^ 1865, 1866, and AaU RegUter^ vol. ii. p.
75 ; De La Rue, Stewart, and Loewy, Researchet on Solar Phyeics, First
Series ; Sir J. Herschel, Monthly Notices^ vol. xxv. p. 152.
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262 Mr. HugginSy Observations on the
form, is the irregular broken outline by which they are bounded.
If, however, these smaller irregularities of figure be disre-
garded the granules may be described generally as possessing
a more or less oval form. The granules appear to me not to
be flat disks, but bodies of considerable thickness.
In the interpretation of these bodies it must not be for-
gotten that minute irregularities which appear almost insigni-
ficant in our telescopes would not be little to an observer on
the Sun. If the granules could be viewed from a short dis-
tance they would appear probably as wildly rugged in irregu-
larity of outline as are the clouds of our sky.
Size. — On April 26, the Sun's image was allowed to pass
before the wires of the micrometer placed at a small distance
apart. The interval separating the wires appeared to include
sometimes two and sometimes three of the granules which were
in contact with each other. I found the value of the interval
between the wires to be 2"' 5 9. The average size therefore of
those bodies may be taken roughly at i" in diameter, and the
average longer diameter of the more oval particles at about
i"'^. This estimation SLgrees closely with the size assigned to
them by Mr. Stone.
On some small areas of the solar surface the groups ap-
peared to be composed of granules of nearly the same size,
whilst on neighbouring areas a considerable difference in size
existed between the adjacent granules. Occasionally a much
larger granule was seen which might measure from 2'' to 3'' in
diameter. Many of the granules were smaller than i " in diameter.
Relative position. — On many parts of the Sun the granules,
though they lie near together, are detached bodies separated
from each other by small intervals. These groups of isolated
granules are mingled with tesselated surfaces of bright matter
formed of close aggregations of granules. The forms assumed
by the groups of closely united granules are very various.
Often they appear as nearly round or oval cloud-like masses,
and when in this form have been probably mistaken by some
observers for single granules. Sometimes these groups are
long, irregularly formed bands, suggesting to an observer the
rugged, broken sides of a range of mountains. On April 26,
nearly in the centre of the Sun's disk, I observed a long oval
border of tesselated bright matter, enclosing an area over
which the granules were sparsely distributed. Some of the
more characteristic of the modes of grouping of the bright
granules, which I have observed on different occasions, are
given in a diagram which accompanies this paper.
It is in connexion with these groups that the coarse motf^ling
of the solar surface originates, for the difference in bright-
ness of adjoining areas is produced mainly by the greater or
less degree of closeness of aggregation of the bright granules.
A second cause which contributes to the formation of the
mottled appearance of the Sun's disk is to be found in the
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Bright Granules of the Solar Surface. 263
different degrees of brightness of the material which fills the
intervals between the groups of granules, and between single
granules.
In addition to these phenomena, a careful observer will
notice appearances which suggest considerable inequalities of
level in the bright surface of the Sun. The whole photosphere
appears corrugated into irregular ridges and vales. Over this
uneven surface, not unlike that of a stormy sea, the groups
Diagram of the Distribution of the Bright Granules on the parts of the
Sun which are free from Spots.
of granules which have been described are irregularly distri-
buted.
Superposition? — I have not been able to satisfy myself whe-
ther the material of the photosphere immediately beneath the
bright granules consists of an aggregation of separate particles.
The appearances presented suggest that this matter is lower
(nearer the Sun's centre), and that generally the granules are
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264 Mr. HugginSy Bright Granules of the Solar Surface.
bodies of considerable thickness, elevated above it, and sur-
rounded by gaseous matter which is non-luminous in compari-
son with the extreme splendour of the granules. So superior
in brightness are the granules, that the exterior layer, which is
composed exclusively of them, must be regarded as the source
of nearly the whole of the light, and probably also of the heat,
which the Sun emits. Except in the penumbra of a spot,
under the influence of unusual currents, I incline to the opinion
that the bright granules are not superposed on each other as
long as they remain recognisable as such.
The phenomena would be well represented if we might
suppose that the granules are recently condensed incandescent
clouds, that they slowly sink, merge into each other, become
less and less luminous, and gradually dissipate into compara-
tively* non-luminous gas. The dark pores would then be repre-
sented by the portions where complete vaporization bad taken
place.
Nature. — Mr. Dawes states that, after years of careful
observation of these bright bodies, he considers them to be
*' merely different conditions of the surface of the compara-
tively large luminous clouds themselves — ridges, waves, hills,
knolls, or whatever else they might be called — differing in
form, brilliancy, and probably in elevation." I would venture
to differ from this distinguished observer only so far as to
suggest that the bright granules were originally separate
clouds, though it may be that their under surfaces soon begin
to unite with the less luminous stratum of clouds beneath them.
I cannot express the ideas suggested to myself by observa-
tions of the Sun more accurately than in the words of Sir
John Herschel — **That it is hardly possible not to be im-
pressed with the idea of a luminous medium intermixed but
not confounded with a transparent and non-luminous atmo-
sphere.'*
The extreme mobility and other phenomena of the bright
matter suggest that it is present in the form of cloud.
The knowledge which the spectroscope affords of the che-
mical and physical constitution of solar matter, together with
the phenomena of terrestrial flame, would suggest that in the
greatly different powers of radiation possessed by matter in the
solid, liquid, and gaseous state, combined with the processes of
condensation and revaporization, a feasible explanation might
be found of solar phenomena. However, the law of exchanges,
for which we are greatly indebted to the original and impor-
tant researches of Balfour Stewart, shows that in the case of
the Sun, if we suppose it to be, at the least, equally hot through-
out its mass, the gas near the surface would not appear dark,
as the umbra of a spot or a dark pore does, because its own
feeble power of emission would be supplemented by its power
in the inverse ratio of transmitting the radiation from the gas,
or from the photosphere behind it.
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Lord OxmaniowTiy Description of an EqtuUoreal Clock, 265
At present, therefore, we do not appear to be able to explain
satisfactorily the small brilliancy of the material between the
bright particles, and of the darkness of the pores, which, like
the umbra of a spot, appears to be at a lower elevation than
the bright matter. It has been recently suggested that the
dark umbra of a spot originates in a lower temperature pro-
duced by a down rush of cooler gas from above. It is of impor-
tance to know whether this hypothesis can be made to afford a
probable explanation of the numerous dark pores and the small
brilliancy of the material between the groups of bright granules.
If the granules are incandescent clouds, their general oval
form may possibly be due to the influence of currents. We have
to seek, besides the conditions connected it may be with the
high temperature of the Sun, or with some peculiarity when in
the gaseous state of the substances present in the photosphere,
in consequence of which there exists a general approximate
uniformity of size, of form^ and of mode of grouping of these
incandescent bodies.
Description of an Equatoreal Clock, By Lord Oxmantown.
The following description of an apparatus for giving an
equable motion to a heavy Equatoreal of 1 8 inches aperture,
may^ perhaps, be interesting to some of the Fellows.
It was constructed last autumn, and its merit, if it has
any, is that it can be very easily made. No nice workmanship
is required; a joiner and plumber can execute the work
with sufficient accuracy.
The motive power is a piece of wood closely fitting a
wooden box containing water, on the surface of which this
piece of wood floats. This float is covered with canvass satu-
rated with pitch, to prevent it from imbibing water, and so
expanding and sticking fast in the box.
It has also pieces of sheet-brass fastened on the edges over
the pitched canvass, to prevent the pitch adhering to the sheet-
lead with which the box is lined. A tube from the bottom of
the box, terminating in a piece of flexible pipe, the extremity
of which is kept at a uniform depth below the surface of the
water in the box by being suspended from the float, allows
the water to escape at a constant rate which is regulated by
a valve in this pipe. (A k) is the box ; (t i) the float, which
is attached to a brass tube (dd), which acts as a guide by
passing through a hole in the cross-piece of wood (ff),
supported by two upright pieces (gg); (nn) is the India-
rubber tube, through which the water escapes ; (o) the valve
to regulate the flow; (m) is a cock, which is closed when
the clock movement is not required; (qq) a second box to
receive the water as it flows out of the first. When we wish
to employ the clock, we, first, pump up water from {q) to (A)
B
Digiti
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266 Li^d OxnunUawfif Description of an Equatoreal Clock,
through (p) and {I) ; secondly, we get the object to be
observed into the centre of the field; thirdly, open the cock (m)
and clamp the sector {t) to the polar axis {z) by means of the
screw (tt); and if the object is not now sufficiently in the
centre of the field, it may be brought there accurately by
turning the nut (c), which draws the sector {t) further from or
nearer to the float, by bending the spring {to).
The accuracy of this clock depends, to a great extent, upon
the care which is taken to make the sides of the box parallel
and flat, so that the horizontal section may be the same at all
levels, and to fit the float to it carefully, so that the interval
between the float and the sides of the box may be as small as
is consistent with absence of friction. Let a be equal to the
area in square inches of horizontal surface of float, and —
area of interval between the float and sides of the box ; then,
if the float be displaced -^th of an inch from the position of
equilibrium, the surface of the water round the float will be
displaced through — inches ; therefore, if w = weight in lbs.
of I cubic inch of water, the force tending to bring the float
back to its former position = tr . A f — + — j ; whereas, if the
float had rested on a surface of water of infinite extent, the
corresponding force would have been ir . A x — .'. the ratio of
the forces in the two cases = n + i : i. In the case of
the instrument to which this apparatus has been applied,
A = 1 296, and i^ for example, the interval between the float
and sides of the box = -r of an inch, and if the variation of
friction of the polar axis be taken at 3 lbs. (the average
friction being about 7 lbs.), the displacement of the float,
which would have been equal to '064 of an inch on a
surface of water of infinite extent, will become equal to
•064. X j5 ■■ — — « '00044 inches.
, + 36" 145
4X36xij
As the fioat is attached to a wire rope the other extremity
of which wraps round the sector (i) of 28 inches radius, this
deviation corresponds to 7' 51" of space at the equator in the
first case, but only 3''* 2 in the second case.
Assuming that the flow of the water from the box will be
uniform if the head be uniform, the only remaining cause of
irregularity lies in this, that the overflow is kept at a constant
depdi below any fixed point in the fioat; that point, through
variation of the resistance, not bdng at an absolutely invari-
able distance below the surface of the water in the box ; con-
sequently, the head will vary if the immersion of the float varies.
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Lord Oxmantown, Description of an Equatoreal Clock, z6y
We have seen above that, with a variation of friction of
3 lbs., the variation of immersion = '064 of an inch ; there-
fore (47 inches being the distance of overflow below the
surface of water) the ratio of maximum velocity to mean
= jj ^"^ ^ ^ = l^^2JL^ which corresponds to an angular devi-
ation in right ascension of 3 6" of space at the equator per hour.
In practice, however, when the instrument is accurately
counterpoised and carefully oiled, the variation of the force
required to turn it round in right ascension is probably very
much less than this ; and if between one night and the next
the friction increases through viscosity of the oil, the rate is
easily corrected by means of the valve (0).
This clock has been used for micrometrical observations,
and answers perfectly ; but how far for spectroscope purposes
it will bear comparison with other contrivances, has not yet
been ascertained.
The accompanying figure has been drawn on a scale of
J inch to I foot, with the exception of the sector {t) and the
weight {s\ which keeps the rope {x) extended ; these two parts
having been drawn on a reduced scale, and in a different
position to save space.
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268 M. Struve, on the Satellite of Sirius,
On the Satellite of Sirius. Bj M. Otto Struve.
Two years ago I had the honour to communicate to the
Royal Astronomical Society the first results of my micrometrical
measures of the satellite of Sirius^ discovered by Mr. Alvan
Clark. Though at that time the comparison of the observa-
tions made in 1 864 with those of the preceding year strongly
favoured the supposition that the small star did not participate
in the large proper motion of Sirius^ and, consequently, was
not physically connected with it, I indicated the reasons which
induced me to discuss these appearances, and suspended there-
fore the judgment about that conviction at least until the next
year, when the differences between the orbital motion and the
relative motion in the supposition of a merely optical juxta-
position would have increased to nearly the double amount.
At present, after having two years' observations more, we are
enabled to submit the question to a stronger examination.
The following list contains all measures that I have pro-
ceeded until now to make on the satellite, after having excluded
those days on which the state of the atmosphere was indicated
as so unfavourable that it did not admit an accurate measure of
the distance: —
Poeltion Angle.
Dftte.
1863*21
63*21
Sid. Time,
h m
7 30
7 11
Power.
309
309
DifUnceB.
10*30
9.99
Observed.
81-2
Corr.
82-0
83*0
64*18
64*24
64*24
6 37
7 11
7 33
309
309
412
11*22
xo*8o
10-73
75-»
75-6
74-3
76*7
77-4
75-3
65*17
65*24
5 45
8 20
(300)
(300)
IO-39
10*80
76*0
73-8
77*3
77-0
66*19
66*20
66*23
5 55
656
7 4
309
309
309
II '20
10*90
10*70
73'3
74-4
73*5
74'7
76*1
74'7
The column headed '' Corr.'' gives the position angles cor-
rected for the systematical errors, as deduced from my ob-
servations of artificial double-stars. It might be remarked on
this occasion, that by later researches these corrections are
proved to have full strength, as well for natural double-stars
in all zenith distances, as for artificial ones near the horizon.
Concerning my observations, I have further to say that those
of the spring, 1 865, have been made at Rome, where Father
Secchi had kindly offered me for that purpose the use of the
excellent 9-inch refractor of the Observatory of the Collegio
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M. Struve, on the Satellite of Sirius» 269
Romano. For the correction of these Roman position angles, I
have employed estimated values of the magnifying powers. A
small error in this supposition would be of no consequence.
The arithmetical means of each year's observations are —
1863*21 ( = 10*15 P = 82*50 2 days.
64*22 10*92 76*50 3 „
65*20 io*6o 77*15 » ft
66*21 io*93 75*15 3 „
Adopting now the same weight for these four results (a
supposition that appears necessary if we admit for different
years different constant errors of estimation with regard to the
centre of the bright star), the method of least squares conducts
us to the following formukd for a uniform rectilinear relative
motion in the course of three years : —
a » » a
p ^+ (10*186 Ip 0*193) + (0*121-1-0*046) (t - 1863*0)
? =+ ( 1*523 H^ 0*^93) + (0*429 ip 0*046) (t— 1863*0)
p and q being the rectilinear co-ordinates of the satellite from
the principal star. From these formulse we deduced the ob-
served change for three years ; in distance = -|- o"'63 ; in
position angle =— 6°*38.
If the small star formed only with the large one an optical
double star, the mean proper motion of Sirius would have
changed in three years the relative distance by + 2''* 5 6, and
the angle of position by —i 5^*02, — values that might be in-
creased to +2"* 8 1 and — i6°'i7, if we introduce the ascer-
tained inequalities of that proper motion. Evidently our
observations do not agree with similar changes ; therefore this
hypothesis must henceforth be given up.
Moreover, the excellent investigations of Dr. Auwers
{Ast. Nach., No. 1 506), on the orbital motion of SirtuSy de-
mands for the disturbing body in the indicated interval an
increase of the distance by o"'55, and a diminution of the
position angle by 5°* 31 ; values agreeing so nearly with those
deduced from our micrometrical measures, that we scarcely can
doubt that the satellite discovered by Mr. Alvan Clark is really
the disturbing body.
The distance itself cannot form in this case a criterion for
the identity, for the irregularities of the proper motion could
only furnish the distances of the common centre of gravity.
The distances of the disturbing body, as given by J)r. Auwers,
must therefore have been derived from a supposition of the
relative masses of the two bodies. Putting rf = 3*05 A (A
being the distance of the centre of gravity). Dr. Auwers, it
seems, has adapted the supposition on the masses to the dis-
tances of the satellite, as observed before his Note of 1864 was
Digiti
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270 M. Struve, on the Satellite of Sirius.
drawn up. Our measures agree so nearly with the supposi-
tion that the mentioned relation would only be changed into
<f = 3-087 A. Of course, even a considerably more important
change in this supposed relation, would affect the change of
the distances, during the short interval of our observations,
only by very small quantities.
With regard to the position angles, on the contrary, not
only their changes, but also their values themselves, as mea-
sured on the satellite, must agree with those deduced for the
centre of gravity of the system, if really that satellite is the
body that has produced the irregularities of the proper motion.
Here we have the following comparison for our yearly mea-
sures: —
o
1863*21 Str. — Auw. « — 0*96
64*22 —5*11
65-20 — 2*73
66'2X — 2'93
This near agreement is certainly one of the strongest indi-
cations for the supposed identity. In the mean the difference
is — 2° '94, which at the mean distance \o"'6^ corresponds to
— o''*55 in space. I do not think this difference can be attri-
buted to the accidental errors of my observations, and even the
supposition of constant errors of estimation with regard to
the centre of the bright star as depending from the sensibility
of the eye for the colours of the atmospheric spectrum of Sirius,
is at least rendered much less probable by the circumstance
than my Roman observations, where that star in its higher
elevation did not offer any trace of spectrum, very nearly agree
in amount and sign with the mean of the other three de-
terminations. Therefore it seems that in this respect Dr.
Auwers' theory is still susceptible of a small correction. That
such a correction might be desirable will certainly not appear
surprising, if we consider the unequal qualities of the nume-
rous observations from which he has derived the disturbances
of the proper motion.
Admitting then that the observed satellite is identical with
Bessel's obscure body, the above given relation d = 3*087 A,
indicates, that its mass must be estimated approximately half
that of Sirius itself. If both bodies had the same physical
constitution, this relation of the masses would assign -to the
globe of the satellite a diameter only 1-26 times smaller than
that of the principal body, and therefore, considering the ex-
traordinary brightness of the large star, we would be induced
to place also the satellite in the first class of magnitude. With
this conclusion the observed brightness of the companion forms
a manifest contradiction. It is commonly said to be of the 9th
or loth magnitude; and only in the Spring of 1864 I have
noted it once as of the 8th magnitude, probably on account of
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Mr, Buckinghaniy Observation of BiekCs Comet, ij i
an extraordinary favourable state of the atmosphere. Hence
it follows that, to maintain the identity, we must admit that
both bodies are of a very different physical constitution. That
the light of the satellite is gradually increasing, as I was in-
clined to suppose from the comparison of my observations of
1864, with those of 1863, has not been confirmed by later
observations ; but in our latitude the estimation of the bright-
ness depends too much from the condition of the atmosphere to
admit of an accurate judgment in this respect.
PulkovOf April 15, 1866.
Supposed Observation of Biela^s Comet.
By James Buckingham, Esq.
At our evening Meeting in March, an inquiry was made
^ if Biela's Comet had been seen ; " having mentioned an ob-
servation I obtained on November 9 last of two bodies which
were supposed by me to be those of that Comet, our President
requested that "details should be furnished to the Society."
But business affairs caused me to leave London the following
day, and I have only returned a few days since, and now beg
to communicate the observation, viz. —
Comets + Star.
IHfference of R.A.
h m B
Nov. 9, 1805, at 9 32 6.M.T. A + 28 and was some minutes N. of B.
B + 37'75 s&me decl. as ^ comparison.
h m 8 o /
^ a is iith or 14th mag. 23 18 35 R.A. 77 25' x N.P.D.
Deduced place of A ^3 19 3
B 23 19 i2'75 77 *5
Owing to clouds, a second position could not be obtained.
It may be necessary to explain why no better observations
could be secured, having usually at hand well-appointed means.
But having been many weeks away in Scotland, returning only
in the beginning of November, I was favoured with Mr. Hind's
Ephemeris of Biela, and sought several nights with my 9-in.
Equatoreal (by Wray, and which is a very fine one) unsuccess-
fully, I therefore put up my 20-in. object-glass (the instrument
having been out of use for several months, for some alterations
of the mounting, and was only approximately in the meridian),
after searching near the predicted places, in sweeping found
two round vapory bodies near each other ; after watching
several minutes motion was detected (from n.f. to s.p.) of the
small one, which appeared most condensed, but without any
Digiti
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272 Mr, Stonty on Kirch* 8 Variable in CoUo Cygnu
sign of nucleus, but yet with nearly defined outline. I had no
micrometer, but only a pair of thick cross -wires in the eye-
piece (negative), which are seen clearly against the sky ; and
observing a small star ^^a," apparently on the same parallel
as the brightest object; got some transits and approximate
positions without being able to determine their accurate ones,
but the star a was nearly north of 70 Pegasi ; therefore went
to my 9-in. Equatoreal, but could not see any trace of the new
objects. On returning again to the large (20") instrument,
again saw both objects, and the one B I thought had moved
yet further and past a very minute star, in the same direction
as before; biit clouds came on, and no opportunity occurred, as on
1 2th November I left London, and did not return till the 23rd,
when I again searched, but could not find either of the new
objects, but found the star of comparison and determined its
place, and having made a rough ephemeris, by using the ob-
served differences on November 9 and Mr. Hind's calculated
places, swept for several weeks at every opportunity. I need
perhaps scarcely say " my conviction is, the bodies observed
were comets ;" and from the circumstance of being near each
other, although closer than calculated, it is presumable, as so
near its orbit, they were Biela's.
A gentleman at the Meeting in March remarked he " had a
doubt if motion could be detected in half an hour." There could
not be the slightest doubt of the fact, and taking Mr. Hind's
ephemeris as very good data, it appears the absolute arc in
that time would be about 26 or 27 seconds; a distance
impossible under like circumstances to be overlooked.
I must apologise for the length of this letter, but must
mention I had the honour of an interview with Mr, Hind on
the morning of November 10, who patiently heard my descrip-
tion, was much interested, but had a very strong impression
" the bodies observed could not be Biela, in consequence of the
places not agreeing with the calculated ones, and so close toge-
ther, but that they were nebulae ;" and therefore no communica-
tion was made to the Society, as I hoped to obtain future posi-
tions, but was prevented, as described, by leaving town.
Westmorland Howe, Walworth Commonf
London f S., May 4, x866.
Note on Kirch*s Variable in Collo Cygni,
By E. J. Stone, Esq.
In 1 686 Geo. Kirch discovered that a star in Collo Cygni
was subject to considerable variations of magnitude. This
star was considered by Kirch to be identical with the 5 th-
magnitude star ;c Cygni of Bayer. In Flamsteed's Historia
CcelesHs Britannica will be found observations of a 5th-mag-
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Mr, Stone, on Kirch's Variable in Collo Cygni. 273
nitude star in CygnuSy which is there called x Pygni. This star
is not the variable. Flamsteed's star will be found in BessePs
Fundamenta, No. 2517, and upon it Bessel remarks, ^' Flams-
teedius stellam per ^ designat, sed- stella a Bayero ita dicta alia
est neque reperitur in Catalogo." The neighbouring 5th-mag.
star is contained in Piazzi, Piazzi has followed Flamsteed's
nomenclature. The star in Piazzi xix. 29^, Cygni Variabilis,
6.J mag., would appear to be the star e of Kirch's map. It
certainly is not Kirch's yariable. In the notes to Baily's
Flamsteed^iW be found the following, " 17 Cygni x- M. Bessel
does not think that this is the star designated by the letter x ^^
Bayer's map. But there is no other star of that magnitude
(5th) observed by Flamsteed or Piazzi that comes nearer to the
position there indicated. I apprehend that the error is in
Bayer, as there is no star in the Catalogue either of Ptolemy
or Tycho that will accord with the position he has given."
Baily has been followed in these remarks by Admiral Smyth,
for in Celestial Cycle, page 460, vol. ii. we find, " This extra-
ordinary star has been mistaken for Xy & 5th-magnitude star,
which precedes." A careful comparison of Bayer's map with
that given by Kirch, Philosophical Transactions, No. 343,
171^, will, I think, most clearly show that the variable is
really the x Cygni of Bayer. It would appear that the variable
must have been near its maximum at the time Bayer was en-
gaged on this part of the heavens, and that the variable was
then brighter than the neighbouring 5th-magnitude star of
Flamsteed, to which no letter h|ks been appropriated by Bayer.
This circumstance is to be regretted. Flamsteed's star is conr
tained in Piazzi and many of our modem standard Catalogues,
and is in them called x Cygni. From our having two stars
both called x Cygni many mistakes have arisen. Mr. Pogson,
in his lists of Variables, Radcliffe Observations, 1854, and
Monthly Notices, 1856, Dec. 12, has given the B.A. and
N.P.D. of Flamsteed's x Cygni, instead of those of the variable.
In subsequent lists Mr. Pogson has corrected this error. But
the same mistake will be found in all the editions of Sir J.
Herschel's Outlines, Chambers' Hand-booh, and probably in
other works. I am of opinion that some steps should be taken
to at least palliate the confusion at present existing from our
having two stars called x CygnL No method entirely with-
out objection can probably be proposed. I think, however,
that the least objectionable method would be to call the star
contained in Flamsteed, Bradley, Piazzi, and our chief modern
Catalogues, X\ Cygni, and then to call the variable x% Cygni.
We should thus have for
1866, Jan. I.
R.A.
N.P.D.
X\ Cygni
h m 8
5 mag. 19 41 20*38
56** 34 5^-67
Xi, Cygni
variable 19 45 »5 ±
57 26±
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274 ^^' Father Secchiy Spectrum of a Orionis.
Spectrum of u, Orionis. By the Rev. Father Secchi.
The rather too short letter which I wrote, accompanying
the drawing of the spectrum of « Orionis^ has given occasion
to -some remarks and inquiries of Mr. Huggins, which require
some explanation on my side.
First, I must say that there is no slit in my apparatus, as
for the stars it is quite useless and troublesome : the position
of the lines is determined and measured as with the double
stars. The original figure which I sent is made on the scale of
one centimeter to one revolution of the micrometrical screw of
the eye-piece. It would have been very easy to form a table of
such values, but every one can make it, applying a metrical
rule to the original figure. All the large lines have been put
down by micrometrical measures : the smaller have been deli-
neated by separating the wires only for one revolution, and
putting them at the due place. The scale being large, no chance
of error exists.
What Mr. Huggins says, that the colours in my figure are
not right, is true ; but this is an effect of artificial light which
changes the tones of the colours; they ought to be omitted
altogether. To fix the lines d and c, I have made use of a
spectroscope with slit, and lights of sodium and magnesium ;
therefore they are correct.
The chief point of difference in my spectrum and that of
Mr. Huggins lies in the band indicated with the letter s in my
figure, which is placed by me^ nearer to ^ than to S, while in
Mr. Huggins' it is quite the opposite ($ is 1 1 5 1 of H). This
difference is so great that no micrometrical measure could be
necessary to acknowledge it.
Not trusting to myself only, I have asked several other
persons to try the position, and they agreed with me. I have
therefore nothing to correct in my drawing, which was made
before seeing those of Mr. Huggins', and carefully verified
several times afterwards.
I do not say that there is a mistake of Mr. Huggins : on
the contrary, I beg him to verify the measures. As he says
that the nebulous band ending with the strong line 1069*5,
then he gives perfect reason to me ; since this is exactly the
band which is controverted, and which I have not seen ; but,
instead of it, I have seen one in the place nearly mo of his
scale.
We are, therefore, agreeing perfectly in the deficiency of
the band ending 1069*5, but he must inquire if this is not
appeared in the place 1 1 1 o of his scale.
I did not intend to intrude into the discovery of Mr. Hug-
gins in the lines of Sirius and Rigel, but only to confirm his
discovery. My observation is rather more detailed, since, for
the intervals of the lines of Sirius and Rigel, I have been able
to fix the proportion of 6| to 4f , As to the similarity of these
L
Digiti
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Mr, Htiggins, on a New Star. 275
spectra with those of Pliicker, I have nothing to retract ; the
number of lines between the red and blue of the ring in Sirius
and in Sulphur is most nearly the same.
Rome, April 16, 1866.
On a New Star, By W. Huggins, Esq.
On May 1 6 I received a note from Mr. John Birmingham,
of Tuam, in which he informs me that, on the night of May
I zth, he saw a new star near i Coron^e B. He describes the
star as " very brilliant, of about the 2d mag." The same day
a letter arrived from Mr. Baxendell ; he observed the star on
the 15th, and found it to be fully equal in brightness to
/3 Serpentis or y HercuUs.
On the night of the i6th, I and Dr. W. A. Miller examined
the spectrum of this strange star. The results of our observa-
tion were communicated on the 1 7th to the Royal Society.
On the 16th, the star was brighter than s Coroner B, fully
•5 mag., perhaps 75 mag. brighter than s. On that evening a
very faint nebulosity was seen extending some little distance
round the star, and gradually fading away at its outer bound-
ary. A comparative examination of neighbouring stars showed
that this appearance of nebulosity was due to the star itself.
On the evenings of the 17th, i8th, 19th, and 2i8t, no certain
indications of a nebulous light about the star could be detected.
The spectrum of this star is very remarkable, and leads to
unexpected conclusions as to its physical condition.
The light of the star is compound, and has emanated fi*om
two different sources. Each light forms its own spectrum.
The principal spectrum is analogous to that of the Sun. The
portion of the star's light represented by this spectrum was
emitted by an incandescent solid or liquid photosphere, and
suffered partial absorption by passing through an atmosphere
of vapours existing at a temperature lower than that of the
photosphere.
This absorption-spectrum contains two strong lines, a little
more refrangible than C of the solar spectrum ; a shaded group
of lines extending nearly to D ; a faint line coincident with D ;
numerous fine lines up to about the position of h of the solar
spectrum, where a series of groups of strong lines commences
and extends as far as the spectrum can be traced.
The second spectrum, which in the instrument appears to
be superposed upon the one already described, consists of five
bright lines. This order of spectrum shows that the light by
which it was formed was emitted by matter in the state oi gas.
One of these bright lines is in the red at the position of
Digiti
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276 Mr, Huggins, on a New Star.
Fraunhofer*s C. The brightest of the lines coincides with F ;
a little beyond this is a fainter line ; near this line a fourth
occurs, which is either double or undefined at the edges. la
the more refrangible part of the spectrum, probably not far
from G, a fifth bright line was seen by glimpses.
On the 1 7th I observed this spectrum of the star simul-
taneously with the bright lines of hydrogen produced by the
induction spark. The brightest line coincided with the centre
of the expanded green line of hydrogen. Apparently the red
line also coincided with that of hydrogen, but the faintness of
the star spectrum did not permit the coincidence to be observed
with certainty.
These bright lines are all much more brilliant than the
corresponding refrangibilities of the continuous spectrum over
which they fall. We must, therefore, conclude that the tem-
perature of the gas by which the light, consisting of these five
refrangibilities only, was emitted, must be much higher than
that of the stellar photosphere from which the principal part
of the star's light has emanated.
On the 17th, 19th, and ^ist, the spectrum of the star was
again examined. No important changes had occurred. In the
faint spectrum of the fading star, on the 21st, both spectra
could be seen. Some additional groups of absorption-lines are
probably present in the continuous spectrum, but the gaseous
spectrum is not changed otherwise than in the diminution of
its brilliancy. The sudden blazing forth of this star, and then
the rapid fading away of its light, suggest the rather bold
speculation that, in consequence of some great internal con-
vulsion, a large volume of hydrogen and other gases were
evolved from it. The hydrogen, by its combination with some
other element (the other bright lines do not coincide with
those of oxygen), giving out the light represented by the
bright lines, and at the same time heating to the point of vivid
incandescence the solid matter of the photosphere.
The grouping of the dark lines of the absorption-spectrum
is similar to that which characterises the spectra of « Orionis
and /3 Pegasi, stars, in the atmosphere of which no hydrogen
exists.
We have found that several of the more remarkable of the
variable stars which have an orange tint have spectra similar
to those of « Orionis, It is worthy of notice that all the white
and bluish-white stars have spectra in which, on the other
hand, the dark lines due to absorption by hy<i*ogen are very
strong, whilst all the other lines are thin and faint. These
and other observations we have made suggest that hydrogen
probably plays an important part in the changes and physical
differences of constitution of the stars!
The grouping of the lines of absorption of this new star
shows that its colour would be orange, if it were not for the
greenish-blue light of the bright lines, which more than
Digiti
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Mr^ Huggins, on a New Star. 277
makes up for the refrangibilities which have been intercepted
hj absorbent vapours. Mr. Hind writes, " On the 19th, the
star was perfectly white and stellar to my eye." Mr. Bax-
endelFs remarkable powers of observation enabled him to
divine some of the results of prismatic examination which at
that time were not known to him. He writes, " On the 1 8th
I several times received the impression of a bluish tinge as if
the yellow of the star were seen through an overfyingjilm of a
blue tint:'
On the 17th, the star's exact position was obtained at
Greenwich. The Astronomer Eoyal informs me that a me-
ridian observation showed that this strange object "agrees
precisely with Argelander No. 2765 of * Bonner Stern ver-
zeichniss/ declination + 26°, magnitude 9*5." Mr. Baxendell
writes to me, ** It is probable that this star will turn out to be
a variable of long irregular period, and it may conveniently be
at once designated T CoronceJ* Mr. Baxendell gives, in his
letter, the following table of the magnitudes of this wonderful
star: —
" A reduction of all my observations gives the following
results: —
lAag.
1866 h m
May 15 at 12 o G.M.T. T Coronee = 3*6 or 3*7
JO
10 30
tt ft
== ^»
17
II
» ft
-4-9
]8
12 30
t tt
= 5*3
19
12 15
t »»
= 5*7
20
12 30
t t*
= 6-2."
A diagram of the spectrum, taken from the Proceedings of
the RoysJ Society, will, by the permission of that Society,
appear in the next number of the Monthly Notices,
Prof. Gould, in a letter dated Cambridge, U.S., April 20,
1866, addressed to the President, calls attention to a paper by
Mr. Ferrel in the year 1853, in which it is shown that the
action of the Moon on the tidal protuberances produces an
appreciable retardation in the velocity of rotation of the Earth.
Mr. Ferrel's paper, published in the Astronomical Journal^
vol. iii. pp. 1 38-141 (Dec. 8, 1853), is entitled " On the Effect
of the Sun and Moon upon the Rotatory Motion of the Earth."
After some preliminary remarks, the author proceeds as fol-
lows : — ■
" Assuming the Earth to be a perfect sphere, the effect of the
Moon is to raise the waters of the ocean on the opposite sides,
and to cause the mass to assume the form of a prolate spheroid.
Digiti
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278
If the Earth remained a perfect sphere, or if the major axis of
this spheroid coincided with the line joining the centres of the
Earth and Moon, the attraction of the Moon could not affect the
Earth's rotatory motion. But in consequence of the resistance
which the waters of the ocean suffer in their motions, the major
axis of this spheroid forms, with the line joining the centres of
the Earth and Moon, an angle of about 30°; and the well-
known tangential force relative to the centre of gravity, arising
from a difference between the attraction of the Moon upon the
different particles of the Earth and the centre of gravity, and
also from a difference in the direction of this attraction, is
not exactly balanced in its action upon the different sides of the
mass, in consequence of two opposite parts, in which this force
acts in the same direction, being a little more prominent than
the other two on account of the spheroidal form which the
mass assumes. Hence there is a small residual force of the
order a^, which, acting continually in the same direction, has a
tendency to produce a variation in the value of d A.* This
force would act upon the waters of the ocean alone, producing
a western current, and would not affect the nucleus at all if it
did not offer resistance to their motions ; but as soon as this re-
sistance becomes equal to the force, the whole force is spent in-
directly upon the nucleus; and as, by the principle of the pre-
servation of areas, the action of the particles upon each other
cannot change the value of A, the effect is the same as if it
acted directly upon the nucleus."
He then proceeds to a mathematical investigation of the
foregoing effect ; this is presented in what may be thought a
form of unnecessary complexity, in consequence of the assump-
tion of a hypothetical law of density of the solid nucleus if but
the result obtained is
rCsom + 16 w')
where
I + A = Semi-axis major of the spheroid, the semi-axis minor being
B I.
m — Mean density of the Earth.
9»'b Density of nucleus at the surface.
* Of the order of the disturbing forces; A, the moment of rotation, or sum
of the products of each particle into the area described by its radius vector. —
Ed.
t The assumed law is —
Density = »»' + c (i - r'),
r being the distance from the centre (the radius being unity) and c being
so determined that the mean density shall be = m ; or finally
Density « 3 m - a m' - 3 (»i — «»') r'.
Digiti
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279
L =s Moon's attraction at distance unity.
^ — Distance of centres of the Earth and Moon.
a « Angle between line forming the centres of the Earth and
Moon, and the major axis of the spheroid.
nt ^ Angular motion of Earth when not acted on by the disturbing
force*
u » Actual angular motion.
For converting the foregoing formula into numbers the
author writes as follows : —
" Now the attraction of the Earth at the distance of the
equatoreal radius, is 32*148 feet; and putting the attraction of
the Moon -^ of that of the Earth, we shall have
75 X 20922000
in times of the Earth's radius. Assuming that the tide caused
by the action of the Moon in the open sea is two feet, and that
it happens two hours after the Moon passes the meridian, we
shall have A = 2, and the angle a = 30, and consequently
sin 2 a = '66602. We will also put ^ = 60, m = 5 J, and wi'= 2|,
and t=i 100 years =3 3155760000 seconds. These values will
give nt — w=: 50*17 miles for the amount the Earth would
be retarded at the Equator in a century, upon the hypothesis
that the whole nucleus is covered with water. But as the
waters of the ocean do not completely assume the spheroidal
form on account of the continents, which occupy about one-
fourth of the surface, we must deduct one-fourth from the value
of n ^ — tt, and we shall then have for the effect of the Moon in
one century
n/ ~ tt s 37*44. miles (18)
Now if in the equation (17), L be increased or diminished,
h will be increased or diminished in the same ratio ; hence the
effect of any other body in changing the value of n ^ — u will
be as the square of its effect in causing tides. But this effect
of the Sun is ^ths of that of the Moon, and consequently its
effect upon the value of n ^ — m will be A of that of the Moon.
We shall therefore have for the effect of both Sun and Moon,
nt — u^ 44*45 miles ( 19)
If the motion of the Earth were retarded by this amount it
would cause an apparent acceleration of the heavenly bodies in
their orbits, which in the case of the Moon would amount to
84" in a century. And as no such acceleration has been ob-
served above what is accounted for otherwise, the rotatory
motion -ef the Earth must be nearly uniform, and the above
Digiti
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28o
effect of the Sun and Moon must be counteracted bj the gra-
dual contraction of the Earth through a loss of temperature."
And, in conclusion, the author calculates that, to counteract
the foregoing acceleration of 84'' per century, there is required
a contraction of about 1*017 ^^^ ^^ ^^^ Earth's radius during a
century, upon the hypothesis of an equal contraction throughout
the mass.
Leyton Astronomiccd Observations.
In revising the proof-sheets of the above volume, I find an
error in the arrangement of Comet Observations has escaped
my notice; at p. 76, the observations for 1864, Feb. 8, 9, 16,
18, and March i, belong to Comet V. and not to Comet IV.
This is immediately evident by turning to the comparison-
stars at p. 95. C. G. Talmage.
Mr, Barelaif'i Oiiervatorif, Leyton.
ERRATUM IN THE LAST NUMBER.
In the liBt of Fellows elected, for George Hurst, Esq., read George Hunt,
Esq.
CONTENTS.
Pag*
Fellows and Associates elected «49
The Semidiameter of the Moon according to M. Hansen's Tables of the
Moon, compared with the results of the best Observations^ bj M.
Oudemans (translation) ib.
Results of some Obsenrations on the Bright Granules of the Solar Sur-
face, with Remarks on the Nature of these Bodies, by Mr. Huggins 260
Description of an Equatoreal Clock, by Lord Ozmantown 265
On the Satellite of SiriuSf by M. Otto Struve 268
Supposed Observation of Biela's Comet, by Mr. Buckingham . . . . 271
Note onr Kirch's Variable in Collo Cygnif by Mr. Stone . . 272
Spectrum of « Orionia, by the Rev. Father Secchi . . . . * . . 274
On a New Star, by Mr. Huggins 275
Notice of Mr. Ferrel's paper of 1853, " On the Effect of the Sun and
Noon upon the Rotatory Motion of the Earth '' 277
Printed by STiULiiroswAYs and Waldkv, Castle St. Leicester Sq. and Published
at the Apartments of the Society, June 6, x866.
Digiti
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,^r\»- i-Ji^r,'/,
University o-j
MONTHLY NOTICES
OF THE
ROYAL ASTRONOMICAL SOCIETY.
Vol- XXVI. June 8, 1866. No. 8.
Rev. Chablss PRiTCHABDy President, in the Chair.
Ebenezer Little, Esq., 18 George Street, Tower Hill ;
W. H. Bajlej, Esq., 25 Cambridge Square, Hyde Park ;
Richard A. Proctor, Esq., 3 Collingwood Villas, Stoke,
Devon;
Henry AUason Fletcher^ Esq., Millgrove, Whitehaven; and
Thomas A. Hirst, Esq., Ph.D. University College, London,
were balloted for and duly elected Fellows of the Society.
On the Effect produced hy the Angles of Position 0/ Double
Stars on the Results of Micrometriccd Measures of them ;
with a Description of a Method hy which such effect may
he avoided or removed. By the Rev. W. R. Dawes.
Very soon after I commenced my measurements of double
stars in the year 1 830, 1 became aware of a tendency to obtain
a different result in position when the line joining the centrep
of the stars was nearly parallel to the line joining the centres
of the eyes, from that which was obtained when those lines
were nearly perpendicular to eaoh other ; and a still more de^
cided difibrence was found to prevail when those lines formed
a very oblique angle. In discussing the points connected with
these differences it will be convenient to call the position when
parallel to the line joining the centres of the eyes horizontal;
when perpendicular to that line, vertical^ and when nearly half
way between the two, oblique. Thus, a double star whose
angle of position is near 90 , or 270°, would, when on or near
the meridian, have what may be called a horizontal position ;
Digiti
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282 Rev, W. R, Dawes, on the Effect produced
if the position were about o° or 1 80° it maj be termed a verti-
cal position ; and if between 30^ and 60° from the horizontal
or vertical, the position would be oblique,
A tendency to a very considerable difference between hori-
zontal and vertical measurements may exist without the obser-
yer being at all aware of it ; and such a difference may to a
great extent vitiate a large mass of observations without being
suspected ; except perhaps by comparison with the results ob-
tained by other observers. But in such cases there will always
be the great difficulty of determining which are the measures
that have the strongest claim to be considered as true and
standard ones.
In my own case I soon became aware of some difference in
the results, which seemed to arise from the relative position of
the stars ; and the way in which I discovered it was this : — An
oblique position seemed to me quite unsuitable for placing the
wires of the micrometer parallel to the imaginary line joining
the centres of the stars ; and certainly, if it were wished, by aid
of a ruler^ to draw a line parallel to two points on paper, no
one would, I should imagine, prefer to place the points in an
oblique position for that purpose; but would, if possible, place
them either in a vertical or horizontal position. When there-
fore I wished to measure such a star as iBobtis, whose position-
angle was about 56^ from a horizontal and 40^ fh>m a vertical
position, I performed the measurements when the star was
sufficiently to the east of the meridian to bring the components
nearly into a vertical line, and then obtained as nearly as
might be an equal weight of observations when the $tar had
arrived at a western azimuth sufficient to place its components
nearly in a horizontal position ; the large northern declination
of the object permitting the two sets to be made within a few
hours. Between the two results thus obtained I usually found
a difference in the same direction, and pointing decidedly to the
different positions of the star as its cause. I immediately set
to work to devise means for ascertaining the amount of discre-
pancy arising from this cause ; and also, if possible, for cor-
recting the tendency to it. I Considered that this would be
preferable to proceeding with the measures, affected as many of
them must be with an unknown amount of error ; and then en-
deavouring by comparison of numerous results to calculate the
amount of error in particular oases, and from this to devise a
formula which might give a probable correction to all cases in
which it was likely to be needed.
A very simple expedient soon occurred to me, which may
be conveniently expressed in the form of directions to any one
wishing to adopt it. Procure a moderately stout piece of card-
board. Out of this cut a triangular piece of any convenient
size, — two of the sides being as accurately as possible at right
angles to each other. The two acute angles may either be of
45° each, or more usefully of 30*^ and 60*^. In this card make
Digiti
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by the Angles of Position of Double Start, 283
some small apertures; die larger ones with a Terj fine and sharp
punchy and the smaller with a hot needle. It is well to have
several pairs of holes, some of equal size and moderate distance
to begin with, and others, for more advanced practice, of un-
equal size and smaller distance. Supposing the acute angles of
the triangle to be 30° and 60°, it wUl be convenient to desig-
nate the side opposite the angle of 30^ by B (the base), the
other side by P (the perpendicular), and the hypothenuse by^.
In this form of triangle there is no necessity for so many sets
of holes to vary sufficiently the angles of position ; for a great
variation is produced in most of them by merely reversing the
side of the card presented to the observer. The lines joining
the centres of the apertures may be drawn at any angle with
respect to B ; but I should strongly recommend that one set of
each kind (equal and unequal size, and at different distances)
should always be made as exactly as possible parallel to J? or
P ; and also one of each parallel to H, Of course, to prevent
the confusion which might arise from too many sets of holes in
one card, as many cards may be prepared as the observer may
think convenient.
A card thus prepared and set up on the frame of an ordi-
nary window may be viewed with a small telescope in a room
of moderate size. I employed an excellent 2-foot object-glass
by DoUond, aperture 1*6 inch,. mounted in a pretty stout tube,
with another sliding into it having a screw which fitted my
parallel-wire micrometer, also by Dollond. This was firmly
fixed in a stout clip upon a fioor tripod ; the clamp of the clip
holding the tube so tightly as to prevent any accidental rotation
on its axis.
The use of the apparatus is now so obvious as to need little
further explanation. I first began with an equal and moder-
ately wide pair in a vertical position, taking a few measures of it
with the card standing on the side B; and then an equal number
of the same object placed horizontally by turning the card on to
the side P. The means of several sets of careful measures in
each position gave accordant results ; the difierence between
the vertical and horizontal measures, even when not large,
always lay in the same direction ; and thus I was quickly led
to perceive its cause and its amount on objects variously con-
stituted. Having thus determined the existence and the
amount of the errors, I endeavoured to remove the cause of
them by taking measures as accurately as possible in a vertical
position, and then altering the reading of the micrometer 90^
from the mean, the card being also turned from B U) P. This
at once revealed the error of judgment, which I have always
considered to belong to the horizontal and all other positions
rather than to the vertical, which were, at all events pretty
uniformly the most accordant among themselves.
Each observer may, of course, pursue some such plan of
observation on any number of oblique positions ; and thus en-
Digiti
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284 R^' W. R. DaweSf on the Effect produced
deaTOur to divest his judgment of all discrepancies attaching
to them. But it presently occurred to me that such a process
would be unnecessarily long and laborious ; and that at the
same time an equally satisfactory result might be obtained in a
simpler way, namely, by the use of a small prism attached to
the eye-piece between it and the eye. This I accordingly had
done by DoUond ; and found it work so satisfactorily that I
strongly recommended its use in the Introduction to my first
series of Double-star Measures, which was read before the
R.A.S. in 1834, and honoured with a place in vol. viii. of the
Memoirs, This simple contrivance,' so easily managed, enables
the observer to place any double-star in any desired position
with respect to a vertical or horizontal line ; and in my" own
observations I have frequently resorted to it even with stars
whose position is not very oblique (as e.g. Castor and yLeonis),
in order to assure myself that I still retain the uniformity of
judgment which I acquired by practising with' the artificial
stars in the cardboard. I have however confined myself en<*
tirely to the vertical and horizontal positions.
It is a remarkable circumstance that that excellent and ex*
perienced observer, M. Otto Struve, after having accumulated
an immense mass of double-star measures, became aware that
they were liable to a considerable error, in many instances at
least, from obliquity of position ; and in order to ascertain its
amount and the law by which it was governed, he instituted a
careful series of measures of artificial double stars set up at a
considerable distance from the Poulkova Observatory, and
observed with the large equatoreal. This is, of course, an
incomparably more laborious plan, and can be pursued only
under extremely favourable circumstances. There must also
exist other rare and peculiar combinations to render it at all
possible to affix suitable objects at a sufficiently great distance
and in a suitable light, &c. The results however, procured
with great care and labour, proved very important, and showed
the necessity in many instances of applying a considerable cor-
rection to the observed angle, and a formula is given for its
computation. In his paper on this subject he refers to my re-
commendation of the use o£ a, prism; but raises the objection
that a prism might introduce errors of a difierent kind, and in
every case might injure the quality of the telescopic images.
" This," he adds, " is the reason why astronomers in general
have not adopted the proposal of Mr. Dawes, which under cer-
tain circumstances is worthy of being pursued, because it
might furnish interesting corrections (or modifications, con*
trdles) to the results found by another method."
With reference to this objection to the use of the prism,
which would be formidable if well founded, I feel bound to say
that, having during the thirty-five years which have elapsed
since my first proposal and use of it employed prisms made by
DoUond, Merz, Simms, and the late Andrew Ross, I have found
Digiti
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by the Angles of Position of Double Stars, . 285
that BO one of them produced any perceptible deterioration of
the image. I cannot therefore but conclude that this fear has
no foundation sufficient to deter anj observer from the use of
this instrument ; and nothing can be more easy of detection
than ia. fault of this nature. Moreover, the light lost is so small
^hat extremely delicate objects may be observed with it. M.
Otto Struve further states that he is not aware that I have
published any results affording a comparison between the results
obtained with the prism and without it. It is quite true that
I have not published any such; the reason of which was simply
that I supposed the defect was probably restricted to my own
observations, never having at that time (in 1830) heard of any
observer who had detected a similar source of error. Neither
was this point elucidated by any allusion to it in a correspond-
ence which ensued between Sir John Herschel and myself.
I therefore concluded that it was probably peculiar to my own
observations; and having succeeded in correcting the tendency
to it by the method explained in this paper, I did not suppose
that the subject would possess much interest for other obseiv-
vers. Lately, however, my attention has been again attracted
to the subject by a correspondence with one of our best double-
star observers ; and I have therefore thought it desirable no
longer to delay the present explanation of my own successful
meUiod of overcoming the difficulty.
Hopefield Observatory j Haddenhamy BuekSy
SJunef 1866.
Equatoreal Observations of R.A, of Mars and neighbouring
Stars for the Determination of the Sun's Parallax made
with the Equatoreal of the Observatory at Madras in the
year 1862, and Meridional Observations of N,P,D, of
Mars and neighbouring Stars made with the Meridian
Circle. By N. R. Pogson, Esq., Government Astronomer.
(Abstract.)
At the request of the Astronomer Royal, observations of the
Planet Mars were made during the opposition of 1 862, at rising
and setting, with a view of illustrating the method suggested
by him in the Monthly Notices of the Royal Astronomical So-
ciety, vol. xvii., p. 219, and again in vol. xviii.^, p. 277, for the
correction of the Constant of Solar Parallax, rather than with
any hope of being able to realise a trustworthy result, owing
to the very imperfect instrumental means available for such
observations. A similar proposal had been made to Major
Digiti
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286 Mr, N. R. Pbgson^ Equaioreal Observation ^e.
Tennanty Govemment Astf onomer at Madras, in regard to the
opposition in the year 1 860, but had also been prudently de-
cUned by him on the very grounds now urged and foreseen by
the present Astronomer before commencing the series under
consideration.
The instability of the Madras Equatoreal ; its damaged and
shattered condition, owing to the effect of repeated storms,
from the fury of which the worthless folding roof oyer it was
literally no protection at all ; its defective and in part useless
illumination; all combined to render every possible exertion
and precaution alike nugatory, and to reduce the attempt to a
mere justification of Major Tennant's judgment on the former
occasion.
Observations (114 in number) were, however, made, with
20 Comparison Stars, between September 22 and October 28,
1862; and though, for the reasons above stated, the result
could not be expected to possess any actual value, it never-
theless proves clearly that the long -adopted value of the
parallax requires to be increased by a considerable fraction of
itself; and that the method, if effectually carried out by the
aid of better instrumental means, is in itself good, and well
worthy of the utmost care and preparation, when the time shall
again arrive for repeating the measurements of Mars under
more favourable circumstances than those existing at the
Madras Observatory in die year 1862.
The final value of x (Correction to Parallax), viz. +o"*579,
is evidently too large; giving tf = 9"* 156. The Comparisons
of Mars with four of the twenty stars did not enter into the
determination at all, in consequence of these being only taken
on one side of the meridian. All other observations are, how-
ever, included, and possibly a judicious weeding out of all
dubious comparisons might give a better result* It may also
have been wrong to correct only the mean values of «'— « for
refraction and parallax ; each individual comparison, or at
least those of not more than ten minutes apart, being better
taken separately. It is not, however, imagined l^at much im-
provement would have arisen from so vastly extended a system
of corrections ; and the failure of the attempt is probably at-
tributable to the too low magnifying power employed (only 63)
rather than to any other cause; and much as the unsatis-
factory result is regretted, the author exerted his most earnest
endeavours to do the best he could with the very imperfect
and unsuitable instrumental means available. He remarks
that any suggestions as to a better mode of treatment of the
observations would be thankfully received and acted on at the
earliest opportunity.
Digiti
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Occidtations of Stars by the Moan Sfc, 287
Oceultations of Stars by the Moon^ and Phenomena ofJu-
piter^s Satellites^ observed at the Royal Observatory^
Greenwichy from April 1864 to April 1866.
Oceultations of Stars by the Moon,
Day of Ob-
serTBtion.
Moon's
Limb.
MMn Solar
Time.
ObMTTW.
1864.
June 26
62 Pisdum, disapp.
Bright
h m a
13 22 29*6
R.
{a) ^ Piscium, disapp.
Bright
13 40 71
R.
{b) 62 Piscium, reapp.
Dark
14 II 32*6
R.
{b) ^ Piscium, reapp.
Dark
14 40 27-5
R.
Dec. 5
K Aquarii, disapp.
Dark
8 34 54-8
J.C.
(c) K Aqoarii, reapp.
Bright
9 28 17-9
J.C.
1866.
Mar. 3
S* Tauri, disapp.
Dark.
10 15 20'9
J.C.
July 3
^ Libra, disapp.
Dark
9 58 i8-o
J.C.
{d) •* Librae, reapp.
Bright
10 so 33-2
J.C.
8
(e) (1 Sag^ttarii, disapp.
Bright
9 21 8*0
J.C.
Nov. 4
V Tatiri;, reapp .
Dark
,0 36 44'9
J.C.
Dec. 30
ii5Taiiri, disapp.
Dark
7 34 5«-9
L.
1806.
Feb. 23
130 Tauri, reapp.
Bright
6 23 46*1
C.
»7
h Leonis, reapp.
Bright
9 435
C.
(a) The star appeared to hang about 0**7 before disappearance, (fi) In-
stantaneous, (c) A little separated from the limb when first seen, {^d) The
star appeared to hang on the limb about i* or {* after reappearance, (e) A
yerj unsatisfactory observation.
Phenomena of Jupiter* s Satellites.
DayofOb-
■ezration.
SateUiU
MMa Solar
Time.
Obsenrer.
1864.
April 14
(/) Eclipse, disappearance
h m 8
13 33 44-2
c.
May 7
(jf) Eclipse, disappearance
13 44 "'3
J.C.
16
(g) Occult disapp. bisection
9 5« 35*4
J.C.
22
III
Eclipse, reappearance
9 34 390
E.
»3
Occult, disapp. first contact
11 41 52*3
C.
Occult, disapp. last contact
11 46 36-5
C.
Eclipse, reappearance
14 9 7'»
C.
29
III
Eclipse, reappearance
13 33 19-1
C.
June 13
Transit, ingress, first oont.
9 X 8*0
C.
„ bisection
9 4 37*6
c.
„ last cont.
9 6 37-1
c.
Transit, egress, bisection
11 20 40*3
c.
last cont.
11 22 40'0
c.
Digitized by Google
—
288 Mr. fVaterstohy on the Change in the
Day of Ob-
MMn Solar
aerration.
SatoUite
Time.
Obserrw
1866
h m ■
May 22
11
(A) Occult, reapp. bisection
13 34 30-7
J.C.
June II
I
(A) Eclipse, disappearance
13 12 178
J.C.
19
I
(h) Transit, ingress, bisection
12 6 54-8
J.C.
zo
III
Edipse, reapp. bisection
12 41 41-9
E.
28
1
{h) Transit, egress, last cont.
10 32 39'p
C.
July 25
II
Eclipse, reappearance
10 41 329
C.
29
I
Eclipse, reappearance
10 20 28*5
T.C.
Aug. 2
III
(t) Eclipse, disappearance
10 4 9-5
L.
Sept 2
II
Occult, disapp. first cont.
7 51 50-5
E.
II
„ bisection
7 S3 ao-3
E.
6
I
(t) Eclipse, reappearance
8 50 51-4
C.
7
III
Eclipse, reappearance
8 43 54-1
E.
H
III
(k) Occult, reapp. bisection
7 34 »6*7
J.C.
(/) Unsatisfactory ; cloudy, (g) Very uncertain ; the image of the
planet bad. (h) The observation very unsatisfactory ; the planet very badly
defined, (t) Somewhat uncertain, the satellite being very ^dnt neuc Jupiter ,
which was low. {k) Unsatisfactory from haze near the horizon.
The initials D., E., C, L., J. C, R., and T. C, are those of Mr. Dunkin,
Mr. Ellis, Mr. Criswick, Mr. Lynn, Mr. Carpenter, Mr. Roberts, and Mr.
Chappell.
On the Change that would tahe place in the Elements of the
Earth^s Orbit by a sudden accession to the Sun^s Mass.
Bj John James Waterston, Esq.
That the appearance seen in the Sun on the ist of Septem-
ber, 1859, ^y ^^' Carrington and by Mr. Hodgson, indicated
an accession to the Sun's mass is no doubt very generally ad-
mitted, but that the amount of that accession can have sensibly
diminished the length of the year is an idea that may perhaps
incur ridicule, not from its impossibility, but because the Green-
wich observations must ere this have detected so remarkable a
circumstance. There seems also to be an impression that the .
fall of such a planet as the Earth into the Sun " would, from
the conversion of its previous mechanical energy, give out an
awful blaze of light, such a blaze as . . .< would scorch up in a
moment all the inferior planets, and probably the Earth also,
with everything upon it" {Monthly Notices^ voLxx. p. 89).
When this is put to test of figures, as at p. 197 of the same
volume, such a ciatastrophe is clearly out of the question. Even
if the blaze were persistent, the general rise of the temperature
could not exdeed 10° or 15°, but it could not be persistent, inas-
much as the extra power of radiation can only act for the short
time taken to traverse the Sun's atmosphere before plunging
under its surface, which observation shows to be not only in-
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' Elements of the Earth's Orbit ^c. 289
candescent but highly mobile as a fluid ; the blaze would then
terminate, and the general temperature of that part of the Sun
be very sensibly increased, yet not so as to increase the radiat-
ing power in a perceptible degree.
Take the extreme case of the whole potential radiating
power of the Sun being thereby raised 1000°, even this is only
y^^^Tjth part of the potential temperature that sends heat to us
sufficient to maintain a general average temperature over the
surface of the Earth of about 500^ above the absolute zero.
Now this proportion of 500° is only ^th of a degree, and this
is the extreme maximum effect that can be reasonably expected
from such a planet fall.
The phenomenon observed on the ist September is thus
quite consistent with what might justly be expected from an
accession to the Sun's mass approaching in magnitude to our
planet. Mr. Carrington describes the intensity of the blaze to
be fully as great as if there had been a hole in the screen at-
tached to the object-glass of the telescope ; fully as great as
the direct unscreened sunlight. Mr. Hodgson describes it as
being most dazzling to the protected eye. Such descriptions
warrant an estimate of intensity several hundred times tiiat of
the normal surface ; enough if persistent to produce a consi-
derable change of climate ; but as persistence is physically im-
possible, nothing of the kind need be looked for. The only
indication of the mass thus added to the controlling centre of
the system which we can become cognizant of is the possible
decrement in the length of the year.
The following is the process of computation I have employed
to ascertain this. The resulting formula, it will be remarked,
is extremely simple in consequence of the excentricity of the
Earth's orbit being small.
If the mass equalled that of our globe the decrement in the
length of the year is 130*. This would cause a difference of
5"*3 in the longitude of the Sun at the end of the first year
(September i, i860), of io"*6 on September i, 1861, and on
September i, 1866, the Sun would be 37'' in advance of the
position given in the Nautical Almanac, If the mass was less
than this the difference would also be less in the same propor-
tion.
In fig. I the major axis of orbit is PSA; the triangle
formed by the Sun, Earth, and aphelion focus is S E F ; the
radius of curvature is R E, and the normal E N.
An addition of -^th to the Sun's mass causes an immediate
I ^
decrement of — th in the length of R E and a change in the
length of the normal, but no change in the direction of R E or
FE.
Suppose a line to be drawn from S, passing through N',
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290
Mr. WaierHon^ on the Change in the
Fig. I.
Kg. a.
the new position of N, and produced to meet F E in /(fig. 2).
Draw/^ J. S F and make F A = F^.
The incremental change in the direction of the major
^ A. The decrement of m%jor axis 2 ) a is
F/a= -^ zip-^zie (p being the perihelion distance P S and
and 2 e = S F). The increment of 2 e is F^ = F /^ and the
decrement o£ zp is /A.
Let represent Z.EFS, a=Z.ESF, and •=Z.E,
fg=zzeix,Fg=^cotfzeix^=:zie, F/sscosecf 2e^A=2^a.
With i a represented by x, we have
axis is If
)x
e
) e » « COB ^
M — »COB^
(I)
(»)
(3)
The radius of curvature ^ is equal to the cube of the nor-
mal « /» \ divided by the square of the semipara-
V sinCA+Lj;
meter * ^- — ^ hence
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ElemetiU of the EarMs Orbit SfC. zg i
The first term
n ^ ' sin X sin (X 4- 1 1) sin' x oot | c •«• sin X cos X ^^ ^
III the triangle S £ N, the angle i being small, we have
-jT^ -6(fi«ir/y)andsin-i--8in(^x + j. ^
hence
cot - » « — : cot X
2 esinx
substituting the value of cot J i in (5) we have
The second term
3?w 3g>x 3g
n r sin X 2 a — r '
2^g 4)6 2ar
s b a
(6)
and since b - >/?TV we have
--3 ^"IT^ ^{nearly)
hence
2)« %x
9 a ' *
(7)
and (5), (6), (7).
L.-AJ--l\otx.li^.t. . (8)
m ( 20— r ay %r~a m ^
Computing this for September i, 1859, with m s 354936
we obtain x^z6\ miles, which, compared with a and the length
of the year, is found to represent a decrement of this length equal
to 130 seconds.
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zgi Mr, E, J, Sioney ObserveUions of the Variable
The change in the values of a, e^ and p, maj be ascertained
from (i), (2), (3), ^ A =- 29". ^e = + 137, ^/? = - 398.
Supposing manj such planet-falls to have happened in the
history of the Sun, and to take place at eyerj different part of
the orbit, the motion of the apses would be cumulative in the
direction of the signs.
If the accession took place in July a; == — 255 and
3e= + 255.
If it took pla<ie in December a? = — 281 and ^e = — 281.
The change of e is (+) at the upper half of the orbit and (— )
at the lower.
InvemeBi, April 25, 1866..
Observations of the extraorditum/ Variable lately discovered
near i Corowe. By E. J. Stone, M.A.
This star has been observed with the Greenwich Transit-
Circle on every clear night since May 17. Its mean place for
1866, Jan. 1, is as follows: —
B.A. N.P.D.
is" 53" 53-8 es^i'sa^-s
In Argelander's Bonner Sternverzeichniss, Zone + 26°,
No. 2765, will be found a star of 95 magnitude, whose mean
place for 1855, Jan. i, was
E.A. N.P.D.
15^53-26-9 63^ 39' 54''
The mean place of this star for 1866, Jan. i, without any
allowance for proper motion, would be
E.A. N.P.D.
'5*^53* 54-5 ' 6^41' 49" r
There is certainly no star of the 9th magnitude near the
variable. It is clear, therefore, that the variable is really the
star No. 2765 of Argelander's Zone -f- 26° ; and that at the
time of observation in ArgelanderVsweep it was below the 9th
magnitude.
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latefy discovered near % Corona. 293
This star was seen, on May 1 2, by Mr. Birmingham, of
Tuam, as a star of the 2nd magnitude.
It was observed by Dr. Schmidt, at Athens, on May 13.
Later on the same evening it was observed also by M. Courbe-
baisse, at Rochefort. Mr. Barker saw it at London, Canada
West, on May 14, and on May 15 it was independently dis-
covert by Mr. Baxendell, of Manchester. Notice of the dis-
covery was now circulated, and the attention of astronomers
directed to the star. It is very remarkable that M. Courbe-
baisse is of opinion that the star could not have been conspi-
cuous to the naked eye on May 11, and he is confident that
such was not the case on May 9. Mr. Baxendell, also, is con-
fident that the star was not sufficiently bright to attract atten-
tion with the naked eye on May 7. It is, however, extremely
difficult to prove a negative, and we may even yet hope to
receive some earlier observations of this star. The number of
independent discoveries of this star is not a little remarkable,
and proves how widely spread is the love of our science, and
with what minute care and knowledge the heavens are nightly
scanned.
The following table of estimated magnitudes contains all the
observations which have come to my hands. It lays no claim
to completeness, and is published merely with the hope of in-
ducing those gentlemen who have made estimations of bright-
ness to publish their results.
Estimatioiui of Magnitude.
§ J I ^ «
ill 1-^ i Is
3 n n oS 2 a's
May 12 2 ...
13 *-3 • 3-»
14 3
15 — 3*6 3-4
16 ... 4*2
.17 ••• 4*9 •• 4*5
18 ... 5*3 4'7 - 4*8
19 - 5*7 - 5-» - S'o
20 ... 6*2 ...
21 6-3
22 7'a 7*» 7*5
13 • 7-a ... 7*8 7*5
24 ... ... 8*4 8*5
*5
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294 ^^« ^' ^' SiaHe^ OhiefvoHon* of the Variable
Ml-
MAyft6
17 8*5
28 8a 8*3
19 8*5
30
3«
June i
2
3
4
5
6
7 8-9 •••
The Greoiwieli obsenrations are based on Argelander's magnitadea.
On May 14 the aky was not in a good state for observing magnitudes.
It appears that the diminution of brightness was for some
time at the rate of aboat half a magnitude a-day : towards
the end of Maj the decrease was far less rapid. I have never
noticed anj traces of nebulositj in the star; it has always
appeared to me to come up quite sharply to focus. This is
also the opinion of all the observers at Greenwich.
On May 19 the Astronomer Boyal's spectrum apparatus,
by which the star-spectra are referred directly to the fixed
lines of the Sun's spectrum, was mounted on the Great Equa-
toreal. On turning the instrument upon the star, it was at
once seen that the ordinary star-spectrum was crossed by four
bright lines; three of these lines were sufficiently bright for
position measurement : the position of the fourth, as laid down
in the diagram, was only estimated. The magnitude of the
star at the time of observation was about the 5 th.
The following excerpts from the observing-books are pub-
lished with the sanction of the Astronomer Royal, who saw the
spectrum himself on May 19 : —
1866, May 19, II^
Observers, E J. Stonei^ and J. Carpenter.
Observations of Spectrum of New Variable in Corona,
The spectrum appeared to consist of two parts: one an
ordinary star-spectrum, in . which were traces of absorption-
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lately discovered near % Coronae. 295
lines; the other, a discontinuous spectrum, consisting of four
bright lines, of which the positions of only three were mea-
sured. The position of the fourth was fixed by estimation.
The visible spectrum extended from about d to half way
between g and h of the solar spectrum. The contrast between
the brightness of the lines and the adjacent parts of the conti-
nuous spectrum was very remarkable.
When the instrument is in adjustment, the reading for the
jUw/ solar Jpae f is 89'-999, »nd *o' of the micrometer carries the
/ index from f to o.
The following are the micrometer-readings for the three
lines measured : —
For I
90-486
From I — 2 =s 5*760
2
84726
From I - 3 = 7-072
3
83-414
May 20, I2^
Observers, E. J. Stone and J. Carpenter.
The following are the micrometer-readings : —
r - ' r
For line I 90*407 From 1—2 5*756
2 84*651
The readings have each been diminished one revolution.
May 22, 11**.
Observers, E. J. Stone and J. Carpenter.
Observation of absorption line in the spectrum of « CorontB
coincident with the solar line f, for verification of zero. The
reading was
90^*003 .
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296 Mr, E. J. SUmm, Observations 8^c.
Obsenration of line i of the spectrum of Variable : the
reading was
observation difficult.
May 23, 1 !*•.
Observer, E. J. Stone.
The lines i, 2, 3, and (4), were all seen, but the positions of
only I and 2 wiere measured.
r
Reading of Micrometer for i — 90*218
2 84-325
For 1—2 5*893
May 24, 1 1**.
Observer, E. J. Stone.
The reading of micrometer for line i was
9o'-346.
Observation very difficult ; strong moonlight, and at times
haze.
May 28.
Observer, E. J. Stone.
The star was now of about the 8*2 magnitude. The
moonlight was overpowering, but I have no doubt about the
presence of the bright line i. I tried several times to coax
the micrometer up to the part of the field where I thought the
line was. The micrometer was at each trial found reading
about 90' ±, or near the true place of the line.
June 7.
Observer, E. J. Stone.
The line near f was certainly still visible, but desperately
faint.
The mean of all the readings for line i is
90»'223.
The reading for the solar line f is
89»-999.
The difference is too small a quantity to be answered for
in observations of such difficulty. It is clear that the line i
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The New Variable near s Coronts. 297
h either identical, or almost identical, in position with the solar
line F. The diagram has been laid down assuming the bright
line to be coincident with f. The unchanged character of the
spectrum, when the star had decreased much below the 8th
magnitude, appears to me a point of much importance.
It was the opinion of Mr. Carpenter and myself that from
the 1 9th of May the brightness of the gaseous and ordinary
spectra decreased in very nearly, if not quite, the same
proportion.
i266, June 9,
Diagram of the Spectrum of Absorption and the Spectrum of
Bright Sines forming the Compound Spectrum of the
temporarily Bright Star near i Coronce Borealis,
This diagram, taken from the Proceedings of the Royal
Society^ is given, by the permission of that Society, in illus-
tration of Mr. Huggins's letter to the Editor at page 275 of the
last Number of the Monthly Notices.
Extract of a Letter from Mr. Graham,
The star in Corona Borealis which has attracted so much
attention is a Variable star of wide range of magnitude, but is
not new. It is marked in Argelander's comprehensive approxi-
mate Catalogue 9J magnitude, and the place, referred to the
mean equinox of 1855*0, is
R.A.
R.A.
h m g
15 53 26-9
Decl.
26 20*1 N.
N.P.D.
63 39-9
become
h m 8
>5 53 54*3
Decl.
li i8-8 N.
N.P.D.
63 41*9
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298 Mr. Chambers^ the New Variable Star,
The place obtained hj the meridian instruments at this
ObserFatorj, on the 17th instant, referred to the same epoch,
is
h m • o / #
R.A. 15 53 53-85 Dccl. 26 18 9*8 N.
N.P.D, 63 41 50-2
Bemarkablj enough, in Wollaston's Catalogue, the epoch of
which is 1790, there is an object recorded thus: —
h m
-O /
R.A. 14 51 ± N.P.D. 63 29 ±
with the foUowing note : —
<* Double (Here. Y. 75) ▼.▼. uDeq. . . dist. 41" 12'" . . .pos. i6°f./.
It is really auadraple, for the small star is double, and there is a still smaller
at about 30^ t . p. the small ones."
This place reduced to 1 866*0 becomes
R.A. 15 54 N.P.D. 63 42
which also accords with the star in question.
Another circumstance worthy of record is that a nebula is
marked on Gary's large celestial globe as nearly as possible in
the very spot occupied by this star, and which is not in Her-
Bchers Catalogue.
Cambridge Obiervaiarp,
zSthMay, 1866.
The New Variable Star near t Coronce.
By G. F. Chambers, F.R.A.S.
I should hardly have ventured upon troubling the Society
with this communication had it not been for some remarks on
the new star, made by Messrs. Hind and Talmage in letters
addressed to a daily London newspaper ; it seems to me that in
dealing with scientific matters every observation bona fide
made, however seemingly discordant with previous ones, should
be placed on record. The following are my notes : — .
May 2 1 . Turned telescope (aperture 4 inches, powers 40 and
60) on the assigned place of the new star, and found the same
immediately. Made a diagram of the neighbourhood, {tt) is
the stranger. It is about equal in brightness to {y\ a star
south of and in the field of % Coronce, but is brighter than (2;),
star south preceding v Serpentis, Hind speaks of the new star
as free from colour, but to my eye it appeared from the very
first moment of my seeing it to have a distinct pale orange
tinge. It also struck me as particular sharp and well defined.
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Supposed Observation of the New Variable Star, 299
Talmage howeTer says the contrary ; that, on the 1 8th at any
rate, it was surrounded by a hazy nebulosity 30'' in extent.
My own idea would be that if ever I had seen a star less likely
under superior aperture to reveal a trace of nebula, this is that
star. I hope to find light thrown on these discrepancies in some
of the many papers which I suppose will be read at the next
Meeting of the Society.
May 22. New star less bright and orange tinge less strong,
but I consider perceptible, though the Rev. T. W. Webb, who
was with me, did not notice it. He quite concurred however
about 'the sharpness of the star's image.
June 2. The star has considerably diminished in size, and
the orange tinge is no longer striking ; I do not however con-
sider the star destitute of a yellowish cast.
The two stars i Coronce and or Serpentis are I see rated in
the Catalogues each as of 4f mag., but it occurs to me as just
worth mentioning that the latter is considerably less bright
than the former.
Attention has, I believe, long ago been drawn to the fact
that no inconsiderable number of the important known variables
present at their maximum red, orange, or yellow lines. It
seems to me that this circumstance is worthy of more notice
than has hitherto been given to it, and I cannot but fancy that
some interesting but recondite physical law lies concealed here
under the surface.
The Observatory, Sydenham, Kent,
June ^, 1866.
On a Supposed Observation of the New Variable near i Corona,
(Extracts from a Letter qfSir J.F, W, Herschel, Bart,, to one qfthe
Secretaries.)
" At the suggestion of the Astronomer Royal, I send you
herewith, for communication to the Royal Astronomical Society,
a sheet pricked off and accurately copied from the original, con-
taining my naked-eye estimations of the magnitudes of all the
stars which I was able to discover on the night of the 9th of
June, 1 842, within the areas of five triangles, marked out by
the stars «, ^ /3 Herculis^ y, fi SerpentiSy u, CoromBy and /3, 3 Bodtis,
*^ Within one of them occurs a star marked as of magnitude
6', that is to say, according to the system of notation adopted,
6{ or 67 magnitude, as distinguished from y'6 (a magnitude
clearly distinguishable by the naked eye in the absence of the
Moon) and whose place, as laid down by allineations with the
neighbouring stars ^, t Corona and x Serpentis, agrees so nearly
with that assigned to the star whose recent outbreak has
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300 Supposed Observation of the New Variable Star.
excited so much attention, that I cannot help believing it to be
the same.'*
<< The sheet I annex is copied from one oot of a great series
of similar ones, forming part of a series of naked-c^e dbserra-
tions for the estimation of magnitudes and detection of variable
stars, carried out in both hemispheres ; in which the heavens
were divided out into 738 triangles, with a design of mapping
into them, seriatim^ every visible star. The working-sheets
were, in each case^ pricked down from Bode's Atlas, and all
the leading stars (including all of the 5th and a great many of
the 6th magnitudes) laid down in that Atlas pricked in."
<< The meridians and declination circle, drawn on a sheet,
correspond, of course, to those in Bode's eharts and to the epoch
of January 1, 1801, adopted in that work. The stars not in
Bode's charts (which are very numerous) were all corrected
with as much care and endeavour at precision as could conve-
niently be bestowed on them in a work of the kind, but of
course their positions are open to a good deal of error. In the
case of the star in question however there can be no mistake as
to the star, there being no other of ecyial brightness within a
degree and a half of its place. If it be not the new star it is a
Variable star which merits attention for its own sake.
" In an old celestial globe by Bardin, in my possession, con-
taining ^ the positions of 6000 stars, clusters, nebulae, &c., &c.,
laid down from the latest observations of Maskelyne, Dr. Her-
schel, the Rev. F. Wollaston, &c., computed and reduced to the
year 1 800,' I find a star marked as 9th magnitude, laid down
exactly in the place of mine of 6th mag."
ColHngwoodf May 28, 1866.
Note, — A portion only of the sheet has been engraved.
The position of the variable is inserted and marked thus :|t .
_j£_
4/3(
ronat
e®*'
4
•escC^oroT
at
6' *
•
4
•
*£
_H
e
s
M «
JS
V (S^rpii
J^
^o"
A»f
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Mr. Browning^ on ^stituting a Reflecting Prism ^c. 301
On the Advantages gained by substituting a Reflecting Prism
for the Diagonal Mirror in a Silvered' Glass Speculum.
By John Browning, F.R,A.S., F.M.S.
In the paper which I read at the Meeting of January 9th,
on a new method of mounting silvered glass specula in re-
flecting telescopes, I recommended the use of a prism, in pre-
ference to a plane silvered glass diagonal mirror, for reflecting
the image into the eye-piece. Since then many objections
have been made to the employment of a prism for this purpose.
It has been said, firstly, that dew is deposited on a glass
prism much more readily than on a metallic surface. Secondly,
that, in consequence of three surfaces, instead of only one, being
brought into action, and the image having to pass through the
glass, thus being influenced by all its defbcts, the difficulty of
making the prism perform as well as the plane mirror is almost
insurmountable. Thirdly, that the prism reflects no more light
than the silvered mirror. This last statement has been made
on Steinheil's authority, whether justly or not I cannot say.
To these objections the reply may be made, that if dew be
deposited on the two front surfaces of the prism, it can readily
be removed while the back or reflecting surface may be her-
metically sealed, and so effectually protected from any deposition
taking place.
Should moisture appear, however, on the surface of a sil-
vered glass reflector, as is well known, it will greatly injure, if
it does not entirely destroy, the film.
It is evident that, any deterioration of the surface of this
mirror will be much more prejudicial than the same amount of
injury to the surface of the large speculum^ from the cone of
rays being concentrated on the small surface ; and its exposed
position near the mouth of the tube renders it far more liable
to be injured in this manner than the large speculum. I have
not made any experimehts to determine the exact amount of
light reflected relatively by the prism and the silvered glass
mirror, because the amount would vary with every silvered
mirror tested ; but I think, simply viewing a white or greyish
cloud reflected by the two placed side by side, will convince
any person that the prism has a decided advantage.
But,.besides this inferiority in reflecting power, the silvered
diagonal mirror possesses another and far more serious defect ;
it does not reflect white light unchanged. I have experi*
mented upon this property of the silvered mirrors with the
spectroscope, and think that I can perceive indications of a
deficiency in the green rays of the spectrum. The simple
experiment represented in the following diagram, however,
shows the change produced by such a mirror more plainly than
any other I have devised.
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302 Mr, Browning, on substituting a Reflecting Prism Sfc.
A is a paraffin lamp ; b, a sheet of white card ; o, a plane
oval mirror silvered on the front or lower surface by Liebig's
process ; d, a prism made of very pure white optical crown-
glass. The sides of this prism, which are presented to the
lamp and card respectively, are ground circular.
The prism and mirror are held, or supported on stands,
about three feet from the lamp, and the height of the lamp
flame from the card.
Under these circumstances two circles of light may be
produced on the card, — one formed by the mirror, the other
by the prism.
On comparing the two, it will be found that the circle
produced by the prism is white, while that produced by the
silvered mirror is strongly tinted with a reddish chocolate
colour. This colour is greatly increased if the experiment be
varied by causing the reflected light to fall on two silvered
mirrors in succession before it forms the circle on the paper.
These are the conditions which obtain in the reflecting
telescope, the large speculum representing the first, and the
small diagonal mirror the second, reflexion.
The eflect of these two reflexions in the reflecting tele-
scope, as usually constructed, is to communicate a reddish
tinge to the stars and planets.
Some difficulty has been experienced in attempting to use
a telescope mounted in the usual way, for taking photographs ;
probably the substitution of a prism for the small diagonal
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Recent Publication . 3 03
mirror would lessen the difficulty which has been experienced
in such experiments.
I have recently had the pleasure of making a very large
reflecting prism, 2 J inches in the minor axis, for our late
excellent President, Mr. Warren De La Rue ; it is now before
you. This prism I have submitted to the severest possible tests,
and I hope its performance will prove that such prisms are
worthy of general adoption.
Note, — Jamin has published an account of some experi-
ments "on the colour communicated to light by successive
reflexions from the surfaces of various metals."
RECENT PUBLICATIONS.
Let og Noiagtig Methods S^c, Easy and accurate Method for the
Determination of the Latitude and Longitude at Mid-day,
together with the Error of the Compass, without the help
of Logarithms. By J. J. Astrand, Director of the Observ-
atory of Bergen. With three Numerical and two Graphical
Tables. Bergen, 1864.
The determinations are eflected by means of two circum-
meridian altitudes and the meridian altitude of the Sun : thus,
if A,, h^y are the altitudes before and after the passage of the
meridian, and ^,, ^^, are the corresponding hour-angles east
and west of the meridian (reckoned in time) ; and if h^ is the
meridian altitude, then the differences h^-^h^ and h^ — A^ are
proportionlal to ^,* and ^^*, and, consequently, the hour-angle
i (^1 " ^) ^^ ^^ mean between the two times of observation is
given by the formula
where ^^ -h ^, is the interval between the two observations.
But the quantity \ (^^ — ^ J is obtained, not by actual calcula-
tion, but by means of one of the graphical tables, which, for
given values of the diiferences, A©"" ^i *"^ ^o""^i> gives the
corresponding value of the coefficient of ^4 + ^, in the fore-
going formula. A correction for change of declination is in-
troduced by one of the numerical tables, and the true local
time at the mean of the two times of observation is thus
obtained. Thus, in one of the examples given by the author
we have
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304
Intenral of the obtemtioiit 44" 36* « a676*
Ao-*i =* 39' *5"
*o-*f = 47 o
Graphic Table I. gives multiplier s 0,022
2676« X 0*022 ... ... =s s^'9
Table III. gives correction - + 5'6
True time ... ... = i"4*'5
which, corrected for the eqoatioii of time and compared with
the Greenwich time, as shown by the chronometer, gives
the longitude. The foregoing is a safficient explanation of the
principle of the method.
CONTENTS.
Fellows elected 281
On the Effect produced by the Angles of Position of Double Stars on
the Results of Micrometrical Measure of them ; with a Descrip-
tion of a Method by which such effect may be avoided or removed,
by the Rev. W.R. Dawes ib.
Eqnatoreal Observations of RA. of Man and neighbouring Stars for
the Determination of the Sun's Parallax made with the Equatoreal
of the Observatory at Madras in the year 1862, and Meridional
Observations of N.P.D. of Ifort and neighbouring Stars made with
the Meridian Circle, by Mr. Pogson. (Abstract.) . . 285
Occultation of Stars by the Moon, and Phenomena of Jupiier*s Satel-
lites, observed at the Royal Observatory, Greenwich 287
On the Change that would take place in the Elements of the Earth's
Orbit by a sudden accession to the Sun's Mass, by Mr. Waterston 288
Observations of the extraordinary Variable lately discovered near c 09-
rmup, by Mr. Stone 292
Diagram of the Spectrum of Absorption and the Spectrum of Bright
Sines forming the Compound Spectrum of the temporarily Bright
Star near t Qtrmue BoreaUt, by Mr. Huggins 297
Extract of a Letter from Mr. Graham ib.
The New Variable near t Conmmy by Mr. Chambers 298
On a Supposed Observation of the New Variable near t CorofUB, extract
of Letters from Sir J. F.'W. Herschel 299
On the Advantages gained by substituting a Reflecting Prism for the
Diagonal Mirror in a Silvered-Glass Speculum, by Mr. Browning 301
Recent Publication : —
Let og Noiagtig Methode &c., by J. J. Astrand 303
Printed by Strahocways and Waldkk, Castle St. Leicester Sq. and Published
at the Apartments of the Society, July 9, 1866.
Digiti
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MONTHLY NOTICES
OF THB
ROYAL ASTRONOMICAL SOCIETY.
Vol. XXVI. Supplemental Notice. No. 9.
Extreict of Letter from Professor F, Kaiser^ of Leiden^ to the
Astronomer Royal, dated i August, 1 866.
From my investigations it appears that your double-image
micrometer has far too little attracted the attention of Astrono-
mers.
The many discrepancies one discovers in the measurements of
double-stars that have been performed by different Astronomers
have induced me, a year ago, to measure the principal double-
stars, as well with your doublerimage micrometer as with the
wire-micrometer. I wished to measure each star with each
micrometer, on at least five different days; but the air was
never so tranquil as was necessary for my measurements, and if I
would make any progress, I was obliged to measure even when
the dispositions of the air made measuring almost impossible.
I have already closed my measurements on several double-stars
with both micrometers, and, as a proof, I give you in the ad-
joining table the results for all the double-stars I measured, of
whid^ the distance is less than 1 2'', with exception only of
two, the measuring of which has taken place under too bad
circumstances. I have not yet had time to reduce accurately
the measurements performed with your micrometer, and, in the
adjoining table, I have provisionally adopted for the value of a
revolution of the screw the constant number 7"' 50. A more
accurate reduction cannot modify the results above a few hun-
dredth parts of a second. The harmony between my fifst re-
sults is greater than generally exists in micrometer measure-
ments on double-8tars,and it would have certainly been still much
greater if the air had not thwarted me. In Mr. Main's measure-
ments with the Oxford heliometer, published in the Radcliffe
Observations, and in those with the heliometer of Konigsberg of
Dr. Augers, published in the Astron. Nachr, No. 1393,! found
sixteen that have taken place nearly at the same time. In eleven
of those sixteen measurements the discrepancies in the distances
are more than o"*25. In yAndrom. the difference is o"-69 ; in
Digiti
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3o6 Exircici of a Letter from Prof. Kaiser ^ ^c.
I Serpentis, o''*90; in n Cassiop. o'''g$ ; and in /8 Cygni over
i"-42
Luther at Konigsberg differed, when using the same
beliometer, sometimes a full second from Peters and Auwers
{Astron. Naehr, No. 1393). Very great differences are alsp
found between the measurements performed with the wire-
micrometer. The great harmony I obtained with two quite
different instruments does prove that the discrepancies must
far more be sought in the observers than in the instruments.
The actual measurements on double-stars appears to me far too
inaccurate for the consequences one will derive from them.
In the screw of the wire-micrometer, delivered hy Mr.
Mens, I found errors that amounted to i'^. A paper on that
micrometer has been printed in the Periodical of the Bojal
Academy of Amsterdam.
BtMT.
WiththoWir«-Mlcroin.
With Bfr. AirfB MIcrom.
Ho.!
Hum.
Epoch.
Dtot.
PoaiUon.
Epoch.
Diat.
PMltiMk.
a7J7
• Eqmilei
1865-85
i-o»
103*0
1865-75
r%8
...
1583
•'AquilK
584
'•34
1 17*6
579
«-44
...
aos5
X Ophinchi
6*50
'•45
22-8
6-53
1-38
26*9
aa6i
rOphhichi
5-68
1-51
247-8
5-57
1-50
250-9
94«
12 Lynda
628
1-64
3165
6-35
«-59
317-3
«S»3
(UnsMajoriB 6-45
208
87-8
6-39
2*10
86-7
2383
5 Lyne
5-85
2-35
142-6
575
2-35
143-4
774
( Orionia
6-21
236
1555
6-11
231
150-9
i«77
tBootU
6-47
263
3H-8
6-50
2-74
3*5*8
138*
f Lyne
585
295
20-6
5*75
312
16-3
H»4
y Leonia
6-24
309
110-7
6-33
3-15
109-9
2909
CAqoarii
5-85
3-n
1589
575
3-34
157-4
«954
1 Serpentia
5-69
3'3
>94*4
5*54
ri8
1923
1009
628
3-30
337-0
6-34
3-23
335-1
1670
y Virginia
6-46
4-OI
1659
6-38
4*3
164-6
738
X Orionia
6-21
409
41-3
6-06
4-33
42-1
2140
« Herculia
569
4-64
115-4
5-72
4-56
115-7
1223
^ Cancri
624
471
214-1
633
4-86
215-3
11 10
« Geminorum
6-27
516
240-8
6-37
5-»3
241-6
1888
I Bootis
646
S»3
298-6
6-42
5- 19
300-8
2272
p Ophinchi
5-68
5-3»
100-4
5-56
5-34
100-9
1 196
I Cancri
624
5'33
318-3
6-33
5-51
318-7
1224
IV Cancri
6-24
5-65
220-0
6-33
5-85
221-3
1864
«- Bootis
6-45
5*73
100-6
6-40
5-68
101-
1965
Z Coronee
569
601
303-1
5-72
6-00
302-7
1998
1 Libra
. 6*49
693
70-5
6-53
7-05
70-0
2760
587
9-67
45*3
5-96
9 -60
45-5
^737
i Eqnnlei
5-85
10-45
764
575
10-26
75-6
TS»
1 Ononis
6-21
10-87
140-6
6-09
11-13
140-5
Digiti
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307
On the Depression of the Barometric Column by the Vapour .
of Mercury. By Gen. R. Shortrede.
It is well known that when a barometer has been stationary
for some days, globules of mercury are to be seen adhering to
the sides of the vacuum part of the tube, and more abundantly
the longer the interval. These globules are formed by the con-
densation of the mercurial vapour which is given off in greater
or less quantity according to temperature, and condense on the
surface of the glass when it becomes colder, in the same way as
moisture is deposited on glass.
The quantity which rises is doubtless very small, but it is
not altogether inconsiderable ; and though usually disregarded,
I believe its elasticity is such as very sensibly to depress the
height of the mercuriid column. In India, where I had a good
deal of experience with barometers, I found I could not get a
true reading till I had condensed the vapour by tilting the
barometer so as to make the mercury click against the top of
the tube. The difference of the readings before and after this
operation was generally from lo to 20 thousandths of an inch,
and on one occasion I found it as much as '023. My barome-
ters were in unexceptionably good order. They had been
repeatedly boiled, one of them more than twenty times, and so
perfect was the vacuum that on being put up after lying for
some hours in a horizontal position, the mercury, by electrical
attraction, would adhere to the top of the tube, and not sepa-
rate till shaken by tapping. The tubes of 32 inches remained
full at Pana, where the usual height is 28, and on the top of
Singi, where the proper height was 26, the tube remained full.
Even in this country the vapour causes a sensible depres-
sion. In the rooms of the Meteorological Society at Edinburgh
some years ago, I said that, in my opinion, none of the barome-
ters were showing the true atmospheric pressure. On taking
readings of two or three of the instruments which admitted
of being tilted there was a difference of from 4 to 6 thousandths
before and after. In the cold weather of winter this depression
may probably be not more than i or 2-thousandths, but in sum-
mer I have no doubt that it will frequently amount to 8 or i o
thousandths.
At Greenwich, on Saturday, I noticed and showed to others
that the vacuum part of the barometer for outside indications
was studded with minute globules, as was also the cistern, the
sides of which under cover were plentifully studded, and on the
iron float was one large globule, occasioned probably by the
vapour, from its higher conducting power, condensing more
readily upon it than on the glass.
The subject is one that seems to deserve investigation, and
if my idea is correct a correction will be required on the regis-
trations photographed at Greenwich.
6 June, 1866.
Digiti
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3o8 Father Secchi, on the Spectrum of Antares.
On the Spectrum of Antares,
By the Rev. Father Secchi.
I I have the honour of presenting the
I Rojal Astronomical Society with a drawing
1 of the spectrum of Antares. This has been
|« made by actual measurement, but on a differ-
I ent' scale of that of « Orionis^ since the prism
« is different ; this prism is one of Amici, with
rS direct vision, but larger, and made by Secre-
^ tan, of Paris. The points of reference are the
f lines D of the sodium and b of the magnes-
J ium. On the figure the lines have been so
J traced that a numerical scale can be ob-
I tained immediately by simply applying a
S metrical rule on the paper; one centimeter
Ik corresponding to one revolution of the screw
1^ of the micrometer.
^ Lately I have found that, for observing
. the most feeble spectra, it is sufficient to
.| place between the object-glass of the tele-
*^ scope and the eye-piece a cylindrical lens of
S two or three inches focus, and behind it
« (between the eye-piece and the cylindrical
£ lens) a prism of Amici of strong dispersive
.g power, as those made by Hofman for his
^ pocket spectroscopes. The image of the star
^ becomes a line beautifully decomposed into its
'Z elementary colours, and the image can be
seen with the common eye-pieces, and the
distances of the lines measured with the com-
mon filar micrometer. With a power of 200 1
have decomposed the bright bands of Antares
into their luminary elements, as with the large
spectroscope. I have also had beautiful
_ spectra, and capable of giving the black lines
^ of the green in some stars of the 8 th and 7 th
% magnitude. Applying this prism to a tele-
'^ scope of 2^ inches aperture, I have been able
•5 to see the black lines of « AquiltB and the
2^ bands of ^9?tore«. This system may be useful
'^ for amateurs, when no absolute but only
^ relative measures of the lines are wanted.
g
^ Romet August i, x866.
M
Digiti
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Capt. Noble^ OccultaHon of Jupiter's Third Satellite, 309
On the Craters of the Moon. By Richard Hodgson, Esq.
Most observers of the Moon have occasionally seen the
hollow craters change their appearance and become solid high
mountains, while the ranges of mountains become hollow cre-
vasses. Generally it has been attributed to a fatigued vision,
and probably by removing the eye from the telescope, in the
course of a few minutes the illusion passes away. Many times
have I been teased with these appearances, and it occurred to
me that the delusion arose from the position of the shadows
being the reverse of what we usually see, and that in the fa-
tigued eye for the time the retina refuses to fulfil its duties and
invert the image, for the instants the craters are seen as moun-
tains ; fortunately this can be easily demonstrated, by applying
a reflecting diagonal solar eye-piece, with a power of 200, to
the edge of the Moon when the craters are prominent, and ob-
serving first on the one side of the telescope in which the cra-
ters appear hollow, and then revolving the whole eye-piece 1 80
degrees, and observing from the other side of the telescope, the
craters are at once transformed to mountains and the ranges of
mountains to crevasses, and no power of will can change them
back to their proper forms, though the revolution of the eye-
piece to its original position at once restores them.
Chingford, Estex^
Sih June, 1866.
OccuUation of Jupiter's Third Satellite. By Capt. Noble.
I last night observed the reappearance of Jupiter's third
satellite from Eclipse at 8** 41*" 30*' i L.M.T. It took place
quite sharply and suddenly; and I had but a short time before
obtained my clock-error and rate very accurately by a transit
of V DraconiSf my transit instrument being very carefully le-
velled mechanicaUy, so as to eliminate all azimuthal error.
Now the Nautical Almanac for this year states that this re-
appearance would take place at 8** 43" 55*'3 G.M.T. ; and
what aggravates this remarkable discrepancy is, that my Ob-
servatory is actually some 17'- 5 East, or fast of Greenwich.
I am desirous that this observation should be recorded in the
Supplementary Number of the Monthly Notices, inasmuch as
it will call the attention of other observers to this very curious
anomaly, and will probably elicit records of observations of
the same eclipse. I have written to Mr. Hind to ask whether
it may not be a blunder of a computer? but shall look out
very curiously for the exact time at which the reappearance
Digiti
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3 lo Mr. Birmingham, New Variable near « Corona.
was seen at Greenwich, assuming that an observation was
made of it. I may just say that I employed my Ross Equa-
toreal of 6i inches focal length and 4*2-inches aperture, with
a power of 154, in observing the phenomenon myself.
Pwtit Lodget Mareifieldf Uckfieldy
August iS, 1866.
The New Variable near t Corona. By J. Birmingham, Esq.
The following extract from a letter, dated Millbrook, Tuam,
July 7, 1 866, addressed to E. J. Stone, Esq., contains an account
of the first observation of this remarkable star.
" On my way home from a friend's house, on the night of
May 1 2, I was struck with the appearance of a new star in
Corona Borealis, It seemed at least fully equal to « of that
constellation in size, and was superior to it in brightness. Its
colour appeared to me nearly white, with a bluish tinge ; and,
• during the two hours that I continued to observe it, I detected
no change in its light or in its magnitude. I did not perceive
the yellow or orange seen by subsequent observers. It shone
quite like the neighbouring stars, without any particular un-
steadiness or flashings. I regret to say that my instrumental
means of observation were limited to an ordinary telescope
with a power of about 25. I could not be sure of the exact
time of my first seeing it, as I was then on the road, some dis-
tance from home ; but I am certain it was between 1 1*30 and
1 1 '45 P.M. Tuam time."
There is contained in the Comptes Rendus of 30th July
and 6th August, 1866, an interesting paper by M. Faye, on
Variable Stars, with especial reference to the temporary star in
Corona. The conclusions are stated as follows : —
'< En resume, les ^toiles dites nouvelles ne m^ritent pas ce
nom, leur apparition presque subite n'est qu'une exageration
du phenomene ordinaire des etoiles periodiquement variables,
lequel repond lui-m^me h de simples oscillations plus ou moins
sensibles dans le phenomene de la production et de Tentr^tien
des photospheres de tons les Etoiles. Ces phenomenes consi-
d^r^s comme successifs dans Thistoire d'une etoile prise a part,
caract^risent les progr^s de son refroidissement et le declin de
la phase que j'appellerai volontiers solaire ou photospherique.
Quand ils se produisent ainsi avec le caractere d'intermittences
irr^guli^res de plus en plus separtes par de tres-longs inter-
valles de temps, ils sont les precurseurs de I'extinction defini-
Digiti
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Mr, Pogsoriy Minor Planet @ Sylvia, 3 1 1
tive, ou du moins de la formation d'une premiere croAte plus
ou moins consistante. C'est pourquoi les phenom^nes de ce
genre ne se produisent que dans les astres d'un ^dat d^jk tr^s-
^ible et n'aboutissent jamais k doter le ciel d*une belle 6toile
de plus."
Minor Planet @ Sylvia. Bj N. R. Pogson, Gorernment
Astronomer at Madras.
A new minor planet, of about iif magnitude, was disco-
vered here on the morning of the 1 7th May, civil reckoning,
by the aid of the same manuscript map which has already
realised me the planets Iris and Sappho, and the four variable
stars R, S, and T Ophiuchh and U Scorpii. The new planet
was, indeed, within the limits of my map of the last-named
object in my long promised Atlas of Variable Stars. The first
night's comparisons were made by means of the ring-micro-
meter of the Hartwell 5 -foot telescope, so long and kindly lent
me by the late Dr. Lee, All the rest were taken t)y the
Boguslawski method, or difference micrometer; to my mind
infinitely the best for all such extremely faint objects. Pre-
suming upon its not having been previously found elsewhere,
I have again selected a name from the list furnished me a few
years back by Sir John Herschel, viz , Sylvia^ the mother of
Romulus.
The new Equatoreal by Messrs. Troughton and Simms
will, I hope, be in use within a week hence, and with it the
planet will be easily observable ; but it is severe eye-straining
lor the Lerebours' Equatoreal, with the Moon above the
horizon.
The Apparent Positions observed so far are as follows : —
Madras M.T.
Mag.
Parallax
App. R.A. Factor.
App. N.P.D.
Parallax
Factor.
Com-
pari-
aons.
1866.
ay 16
h m 8
14 47 51
117
16 l^ 1569 +9-4967
/ '
107 28 48-9
-0-5973
10
16
15 28 12
..
16 IS 14-54 +9-597*
107 28 49*2
—0-5664
10
17
16 10 41
ir6
16 14 2770 +9*68 10
107 28 59-0
-0-5467
16
18
14 22 56
12-0
16 13 45-05 +9-4054
107 29 8-x
-0-6325
18
19
13 37 »7
11-8
16 13 039 +9-2143
107 29 20-8
—0-6466
18
20
13 33 27
I2'0
16 12 14-07 +9*1984
107 29 31-4
-0-6475
20
22
13 28 22
11-9
16 10 40-50 +9-2419
107 29 55-1
-0-6455
20
*3
14 12 46
ir8
16 9 51-90 +9-4565
107 30 8*4
-06257
20
The comparison stars employed have all been observed
with the Meridian Circle of the Madras Observatory.
Madras t May 28, 1866.
Digiti
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312
Minor Planet @ Tkisbe. By C. H. F. Peters, Esq.
{Letter to the Aetronomer Royal.)
The following are observations of an asteroid discovered
here on the 15 th instant, near daybreak, but not made sure of
before the 20th, on account of dark weather intervening :^ —
HAm. CoU. M.T.
B.A.
Decl.
Log<pAr.
leee.
June IS
h m s
15 .. ..
h m ■
10 26 4
/
-17 37 ..
20
13 56 31
*4 39-65
S5 54-8
9*968s
0-8886
21
IX 49 50
24 I 6*67
»4 7*5
0-4355
0-880S
as
13 la 13
S3 50-76
ss so* 8
0*3009
0-8843
»3
1% 57 14
a3 23-87
so 41*0
0-3568
0-8829
H
14 16 a6
so ss 52*94
-17 18 56-9
9-6898
0-8887
Interrupted by other engagements, I have not been able to
accompany these observations with elements. The planet has
the brightness of 1 1 mag., and being still far from opposition,
it may be observed for a long while with meridian instruments.
At the suggestion of a friend, the planet has received already
the name Thisbe, as it is not likely that it has been seen before
elsewhere.
Hamilton College Obeervatory, Clinton^ N,Y,
June 25, 1866.
Digitized by VjOOQIC
INDEX.
Page
Airy, G. B., note on an error of expression in two Memoirs of the
Astronomer Royal in the corrections to the ele-
ments of the Moon's orbit 27
, , description of Abraham Sharp's quadrant 31
, , remarks on the occultation-diameter of the Moon, as de-
termined in Mr. Oudemans' papers 33
, , on the supposed possible effect of friction in the tides in
influencing the apparent acceleration of the Moon's
mean motion 221
, —-f on a method of computing interpolations to the second
order without change of algebraical sign 246
Andes, proposition for a telescope on the, Lieut. Ashe 69
Antares, on companion of, Mr. Freeman 218
' , , Mr. Cottam 244
— — , spectrum of, Pad. Secchi 308
Ashe, E. D., physical constitution of the Sun 62
, , proposition for a telescope on the Andes 69
Associates deceased, list of 103
Encke, J. F 129
Associates elected 249
Astronomy, report on the progress of, in the year 1865-66 146
Barometer, depression in, by the vapour of mercury, Gen. Shortrede . . 307
Birmingham, J., on the new variable near t Corona 3 lo
Brodie, F., some observations on the solar craters which appeared on
September 28 and October 8, 1865 19
Brothers, A., photographs of the Moon 62
Browning, J., on a new method of mounting silvered-glass specula and
diagonal mirrors in reflecting telescopes 77
, — , on the advantages gained by substituting a reflecting *
prism for the diagonal mirror in a silvered-glass
speculum 301
Brunnow, F., ephemeris of Iris for the opposition of 1866 218
Buckingham, J., supposed observation of Biela's Comet 271
Burr, T. W., note on I HercuUs 61
f Canis Majoris, on small star near, Mr. Freeman 245
Carrington, R. C, notice of a recent Memoir of Prof. Krueger of Hel-
singfors on the star-cluster in A. Persei 65
Chacomac, letter on the physical constitution of the Sun 62
Chambers, the new variable near c Corome 298
Chevallier, Rev. T., observations of solar eclipse, October 19, 1865 . . 60
Clock, equatoreal, description of an, Lord Oxmantown 265
Conletary systems, M. Hoek i , 204
Digiti
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3 1 4 Index.
Page
Comets : —
Biela's 241, 271
Encke's 29,63
III. i860 58
1. 1865 , . . 30, 84
Secchi'sof 9 Dec. 1865 67, 81
Cottam, A., Companion to Antare$ 244
Dawes, Rev. W. R., on the effect produced by the angles of position of
double-stars on the results of micrometrical mea-
sure of them ; with a description of a method by
which such defect may be avoided or removed. ... 281
De La Roe, W., award to him of the Lalande Prize by the French Aca-
demy of Sciences 245
— -» , Stewart, and Loewy, notes regarding the decrease of actinic
effect near the circumference of the Sun, as shown
by the Kew pictures 74
— — , — , — , , a comparison of the Kew results of
observations of Sun-spots with those of Hofrath
Schwabe at Dessau for the year 1865 76
Delaunay, abstract of his Memoir on the secular acceleration of the
mean motion of the Moon 85
Donati, E., letter on Comet of 9 Dec. 1865 67
, — , observations and elements of ditto 81
Earth's orbit, on change in the elements of, by sudden accession to the
mass of the Sun, Mr. Water ston 288
Ellery, R. J., places of Comet I. 1865 (great Southern Comet) deduced
from observations made at the Melbourne Obser-
vatory 30
Elliptic motion, on Lambert's theorem for, Prof. Sylvester 27
Errata 220, 280
Faye, M., notice of his paper on variable stars 310
Ferrel, notice of his paper of 1853, on the effect of the Sun and Moon
upon the rotatory motion of the Earth 277
Fellows deceased, list of 102
Burder, W. C 103
Gompertz, B 104
Hamilton, Sir W. R 109
. Lubbock, Sir J. W 118
Smyth, Adnural W. H. : 121
Fellows elected i, 37» 69, 93, 193, 221, 249, 281
Fletcher, J., some remarks on the solar photosphere 23
Freeman, D. A., note on the Companion to Antares 218
, , on a small star near % Cants Minoris 245
Glaisher, J., the November meteoric shower 53
Glasgow Observatory, determination of longitude of. Prof. Grant 37
■ , account of time-signalling operations at 66
Goldschmidt, H., the new star of the year 393 a.c. : documents taken
from the Chinese observations of Ma-tuan-lin,
translated by Edouard Biot, and the remarks of
M. Humboldt in his Cosmos 240
Graham, extract of a letter, on the new variable near c Corona 297
Grant, Prof., on th3 determination on the difference of longitude be-
tween the Observatories of Greenwich and Glas-
gow, by galvanic signals 37
— -, — — , account of the time-signalling operations at Glasgow .... 66
Greenwich observations of oc(;ultation of stars by the Moon, and phe-^
nomena of Jupiter* s satellites * 287
Digiti
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Index. 5 1 5
Pftge
Herschel, A. S., radiant points of shooting-stars 51
' — f , path of a detonating meteor 211
, Sir J. W. F., on a supporcd obsenration of the new yariable
near t Coronw, extract of letters from 299
Hodgson, R.» on the craters of the Moon 309
Hoek, M., on the comets of 1677 and 1683 ; i860 III, 1863 I. and
1863 VI I
, — ,, additions to the investigations on cometary systems 204
Howlett, Rey. P., on the great Sun-spot of October 1865 13
Hnggins, W., on the stars within the trapezinm of the nebula of Orion 71
, — ., reiults of some observations of the bright grannies of the
sokr surfoce, with remarks on the natore of these
bodies 260
■ t — , speetnim of the temporarily bright star near t Corona, ... 275
, — , diagram of the spectrum of absorption and the spectrum of
bright lines forming the compound spectrum of the
temporarily bright star near t Corona 297
f ', and Miller, W. Ai, note on the spectrum of the variable
star « OrionU, with some remarks on the letter of
the Etev. Father Secchi 215
Interpolations, the computation to the second order without change of
algebraical sign, Mr. Airy 246
Jupiter's satellites, phsenomena of, observations by Mr. Talmage ' $7
— — — — , Greenwich observations 287
third satellite, occultation of, Capt. Noble 309 ^
Kaiser, investigations on Airy's double-image micrometer 1D3 /
, same subject, letter to the Astronomer Royal 305 ^
Knott, on the companion to Siriua 243
Lalande Prize, awarded to Mr. De La Rue 245
Loewy. See De La Rue, Stewart, and Loewy
Lunar theory, on error of expression in two memoirs of Mr. Airy, in
corrections to elements of the Moon's orbit 26
, apparent acceleration depending on the effect of the tides
on the rotation of the earth ... 22 1
, , abstract of M. Delaunay's memoir 85
, __ J Mr. Airy on same subject 221
, , notice of Mr. Ferrel's paper of 1853 277
Mars, observations at Madras of R.A. and N.P.D., Mr. Pogson (abstract) 285 ^
Micrometer, Airy's double image, investigations on, Prof. Kaiser ^^%^.^-^Q
Miller, W. A. See Huggins and MiUer. ^-""^ f
Miscellaneous ^ 35
Minor planets, (^ CHOy elements 34
' , @ discovery and elements ib.
, ® Sylvia, Mr. Pogson "311
, ® 7A»ie, M. Peters 312
, Jm, ephemeris of 218
Moesta, observations of Comet III. i860, made at the Santiago Ob-
servatory, Chili 58
Moon, photographs of, Mr. Brothers 62
, remarks on Mr. Oudemans' occultation-diameter of, Mr. Airy . . 33
, semidiameter by Hansen's tables, compared with observations,
M. Oudemans 249
, craters of, Mr. Hodgson 309
Noble, Capt W., occultations of stars by the Moon, observed at Forest
Lodge, Maresfield 63
--, — -_ , occultation of Jupiier*$ third satellite, 17 Aug. 1866 309
Digiti
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3i6 Index.
Obfeiratoriet, aocount of proeeedingB of: —
Greenvich, Royal Obsenratory r 135
Oxford, Raddiffe Obeenratory ib.
Cambridge 137
Edinburgh, Royal Observatory 138
Glasgow , 139
Liverpool ib.
Kew 140
Craaford (Mr. De La Rue's) 142
Wrottesley (Lord Wrottesley's) 143
Tambank (Mr. Fletcher's) ib.
Mr. Huggina' 144
Occultations 6f stars by the Moon : —
observed at Leyton, Mr. Talmage - 57» 8x, 218, 243
Maresfield, Capt. Noble 63
Greenwich 287
Orion, nebula of : -^
Mr.Huggins 7'
Mr. Webb 208
» Orionis, spectrum of 214, 274
Oudemans, the semidiameter of the Moon according to M. Hansen's
Tables, compared with the results of the best
observations 249
Oxmantown, Lord, description of an equatoreal clock 265
Personal equation, in Reading Microscopes, Mr. Stone 48
Peters, C H. P., discovery of Mmor Planet ® Thitbe 312
Pogson, N., equatoreal observations of R.A. of Mars and neighbouring
stars for the determination of the Sun's parallax,
made with the equatoreal of the observatory of
Madras, in the year 1862, and meridional ob-
servations of N.P.D. of Mori and neighbouring
stars, made with the meridian circle (abstract). . . . 285
, discovery of Minor Planet @ Sylvia 311
Quadrant, Abraham Sharp's, description of, Mr. Airy . . • 31
Recent publications 303
Reflecting prism, advantage of substituting for diagonal mirror, Mr.
Browning 301
Secchi, Rev. P., observations of double stars 62
, , on spectrum of « Orionis 214, 274
, , on spectrum of Aniares 308
Shooting stars, November shower, Mr. Glaisher 53
— — , path of a detonating meteor, Mr. Herschel 211
, radiant points of, Btfr. Herschel 51
Shortrede, Gen., the depresrion of the barometric column by the vapour
of mercury 307
Sirius, the companioii of, Mr. Knott 243
, ' , M. Struve 268
Smalley, G. R., observations of Encke's Comet 63
Society : —
Report of Council to forty-sixth annual meeting 94
List of papers, Feb. 1865 to Feb. 1 866 1 52
Library, list of donors to 155
President's address on delivery of medal to Trot Adams 157
Officers and Council for 1866-67 191
Digiti
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Index. 3 1 7
Page
Solar eclipsei Oct. 19, 1865, Mr. Chevallier 60
" , , r, Lord Wrottesley 64
Solar spots, and photosphere, &c. : —
Comparison of Kew observations of Sun-spots with those of Schwabe
at Dessau for year 18651 Messrs. DeLaRue, Stew-
art, and Loewy 76
Obseirations of the bright granules^ &c., Mr. Huggins 260
Physical constitntion of the Sun, Lieut. Ashe 61
. , M. Chacomac 62
Remarks on solar photosphere, Mr. Fletcher 23
Solar craters of Sept. 28 and Oct. 8, 1865, Mr. Brodie 19
Sun-spot of Oct. 1865, Mr. Howlett 13
Spectra of stars, m Orionit 214, 2x5, 274
, new variable near % Corona 275
Star, the new, of the year 393 a-c.^ M. Goldschmidt 240
Stars, telescopic disks of, Mr. Stone 45
, Double, effect of angles of position on results of micrometrical
measures of them 281
, Double or Multiple, ^ HerculiSt Mr. Burr 6 f
, double stars, Pad. Secchi 62
— — ~, cluster in X Perseif Prof. Krueger 65
fi Argtis, Mr. Tebbutt 84
Kirch's variable in CoUo Cy(,n%^ Mr. Stone 272
new variable near i CoromB, Mr. Chambers 298
" , Mr. Graham 297
, Sir J. Herschel 299
. , Mr. Huggins 275, 297
, Mr. Stone 292
^-^— — , Mr. Birmingham 310
Stewart, B. See De La Rue, Stewart, and Loewy.
tone, E. J., on the telescopic disks of stars 45
, — -, on personal equation in Reading Microscopes 48
, , note on Kirch's vaiiable in Collo Cygni 272
,. , observations of the extraordinary variable lately discovered
near 1 Coron<s 292
Struve, O., on the satellite of Sirius 268
Sun, decrease of actinic effect near circumference of, Messrs. De La Rue,
Stewart, and Loewy 77
Sylvester, J. J., on Lambert's theorem for elliptic motion 24
Talmage, C G., observations of occultations of stars by the Moon, and
phenomena of /tiptV^'s satellites, made at Mr. Bar-
clay's observatory. Ley ton, N.E 57
, , occultation of 1 1 5 Tauri by the Moon 82
, , 1 30 Tauri by the Moon 218
, , 3 1 Arietis, 1 866, March 9 243
, , on a probable observation of Biela's comet 241
Tebbutt, J., observations of Encke's comet 29
, — , observations of m Argils 83
, — , elements of Comet I. 1865 84
Telescopes, reflecting, a new method of mounting silvered glass specula
and diagonal mirrors in, Mr. Browning 77
Waterston, J. J., on the change that would take place in the elements of
the Earth's orbit by a sudden accession to tbe Sun's
mass 288
Webb, Rev. T. W., notice of the great nebula of Orion 208
Wrottesley, Lord, observations of solar eclipse, Oct. 19, 1865 64
, Variable,
Digiti
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318
CONTENTS.
Page
Extract of a Letter from Prof. F. Kaiser, of Leiden, to the Astronomer
Royal, dated I Aagust, 1866 .. .. .. 305
On the Depression of the Barometric Column by the Vapour of Mer-
cury, by Mr. Shortrede . . . . 307
On the Spectrum of AntareSf by the Rev. Father Secchi . . . . 308
On the Craters of the Moon, by Mr. Hodgson 309
Occultation of Jupiter* s Third Satellite, by Capt. Noble . . . . lb.
The New Variable near c Corona, by Mr. Birmingham . . 310
Notice of M. Faye's Paper on Variable Stars . . . . . . . . ib.
Minor Planet @ Sylvia, by Mr. Pogson . . . . 311
Minor Planet ® 2%f*6e, by Mr. Peters 31a
Index .. .. .. 313
Printed by Strakoeways aud Waldek, Caatle St. Leicester Sq. and Published
at the Apartments of the Society, October z%, 1866.
Digiti
zed by Google
LIST OF PRESENTS
EECEIVED DURING THE SESSION OF 1865-66,
AND OF
BOOKS PURCHASED WITH THE TURNOR FUND
DURING THE SAME PERIOD,
FORMING
APPENDIX XVII.
To the Catalogue of the Library of the Royal Astronomical Society.
Academy of Sciences of the Institute of France, Comptes L' Academic
Rendus hebdomadaires des Seances, tomes Ix,, Nos. 20 to ^^ Sciences.
26, Ixi., 4to. Paris, 1865-66
Adler, M. N., Memoir of the late Benj. Gompertz, Esq., The Author.
F.R.S., &c., 8vo. London, 1866
AirjY Geo. Biddell, Essays. ■
On the Invasion of Britain by Julius Caesar.
The Invasion of Britain byPlautius and by Claudius Caesar.
The Early Military Policy of the Romans in Britain.
The Battle of Hastings, with Correspondence. 4to.
London, 1865
American Academy of Arts and Sciences, Proceedings, vol. vi., The Academy.
parts 23 to 38, 8vo. 1865
American Academy of Natural Sciences, Proceedings, 1865,
Nos. I to 5, 8vo. Philadelphia, 1865
American Philosophical Society, Transactions, vol. xiii., part The Society.
1, 4to. Philadelphia, 1865
Proceedings, Nos. 71-73, and
List of Members, Jan. 1 865, 8vo. Philadelphia, 1 865
Digiti
zed by Google
3 8o Appendix XVIL
The Society. American Philosophical Society, Catalogue of Library, 8to.
Philadelphia^ 1863
The Academy. Amsterdam Royal Academy, Yerhandelingen, vol. x., 4to.
AmHerdam^ 1864
— , Verstagen en Mededeelingen, vol.
zvii., 8Ta Amsterdam^ 1865
, Jaarboek . . . 1 863-4, 8vo.
Amsterdamy 1863-4
Le Bureau des Annuaire des Mar^s pour Tan 1866, i2mo. PariSy 1865
Longitudes.
The Author. Astrand, J. J., Let og Noiagtig Methode for bestemmelse af
der paakommende Bredde og Langde om Meddagen samt
Compassets Misvisning uden Hjielp af Logarithmer, 4to.
Bergen, 1864
J. 6. Barclay, Barclay, J. 6., Astronomical Observations taken during the
^^' years 1 862-4, ** ^^s private Observatory, Leyton, Essex,
4to. London, 1865
The Society at Batavia, Naturkundig Tijdschrift voor Nederlandsch Indie,
Batavia. jy^^ ^^^ g^^ BataviUy 1864
The Academy. Berlin Royal Academy of Sciences, Abhandlungen, 1 864, 4to.
Berliny 1865
- - Monatsbericht, 1865, Jan.
1866, 8vo. Berliny 1866
Auzug au8 dem Monats-
bericht. Prof. Spoerer iiber die Sonnenflecken, 8vo.
Berliny 1865
The Berlin Berlin, Astronomisches Jahrbuch 1868, 4to. Berlin, 1866
Obsenratory.
The Society. Berlin Society of Physics, Die Fortschritte der Physik im
Jahre 1863, parts i, 2, 8vo. Berlin, 1865
The Board of Board of Trade, Twelfth and Thirteenth Numbers of Meteoro-
Trade. logical Papers published by their authority, 8vo.
Londony 1865
The Academy. Bologna Academy of Sciences, Memorie dell a Accademia,
Serie ii., tomo iii., iv., 4to. Bologna, 1865
— ■ IndiceOenerale, 1850 to 1861,
4to. Bologna, 1864
Digiti
zed by Google
Presents received during the Session 1865-66. 381
Bologna Academy of Sciences, Bendiconto, 1 863-4, ^^^* ^« Academy.
Bolognoy 1864
Bombay, Magnetical and Meteorological Observations made at H. M. Govern-
the Grovernment Observatory in the year 1863, 4to. ^^^ '
Bombay, 1864
British Association for the Advancement of Science, Report of The Associa.
Meeting held at Bath, 1864, 8vo. Londony 1865 ^^^'
Brussels Royal Academy, M^moires Couronn^es et Memoires The Academy,
des Savants Strangers, tome xxxii., 4to. Bruxelles, 1865
. Memoires Couronnes et autres M6-
moires publiees par do. in 8vo., t. xvii., 8vo.
Bruxettesy 1865
■ Bulletins, tomes xviii. xix., 8vo.
Bruxelles, 1864-5
Annuaire, 1865, 8vo.
Bruxelles, 1865
Brussels Royal Observatory, Annuaire, 1865, izmo. The Royal
Bmxelks,i864 ''^^:
Chaeomac, M., Du Soleil et de son Atmosphere, sheet, The Author.
PariSy
Notice sur la Constitution Physique du Soleil,
8vo. PariSy i860
Tracts.
Intensite Comparative de la Lumiere reflechie par la Sur-
face Lunaire et celle de Venus.
Intensite Lumineuse des divers regions du Disque Solaire.
Du Pouvoir Reflecteur du Surface au Sol consid6r6 par
rapport h, celui des Nuages cumulus vivement illumines.
De la Structure et de TOrigine des Yolcans Solaires.
Lithographic sheets. Pari>, 1865
Christiania, Meteorologische Beobachtungen aufgezeichnet TheObserva-
auf Christiania Observatorium, i Band, 1837-63, long ^^'
8vo. Christiania^ 1865
— Meteorologische Jagttagelser paa Christiania Ob- •
servatorium, 1 864, long 8vo. Christiania^ 1 865
Digiti
zed by Google
382 Appendix XVII.
W. R. Birt, Cole, William, Philosophical Remarks on the Theory of Co-
^^' mets, to which is subjoined a Dissertation on the Nature
and Properties of Light, Svo. London^ iSz^
The Coll. Ro- CoUegio Romano, BuUetino Meteorologico del Osservatorio,
"**'***• yqI, iy. jq^o, ^^ yqI, v. No, i, folio. Romuy 1865
W. R. Birt, Comets, Cometomantia, a Discourse on Comets, i2mo.
^^- London^ 1684
The Author. Delaunaj, M., Sur I'Existence d'une cause nouvelle ayant une
influence sensible sur la Valeur de I'Equation Seculaire
de la Lune, 4to. Paris, 1 865
De Morgan, Augustus, On Infinity and on the Sign of Equa-
lity, 4to. London, 1865
Denison, E. B., Astronomy without Mathematics, i zmo.
London, s. d-
Le D^pot G6n. D^p6t G^n^ral de la Marine, Annales Hydrographiques pour
de la Marine. 0^0 r» • o^
1864-5, ^^^' Farts, 1864-5
Chronom^tres, Recherches sur
les, vii. viii. Cahiers, 8vo. Paris, 1864
Instruction pour le Micrometre
Lugeol a Cadran Lori^ux, par M. Bosc, 8vo. Paris, 1865
Instructions Nautiques sur les
C6tes de Corse, par M. Sallot des Myers, 8vo.
Paris, 1865
Instructions Nautiques pour les
principaux parts de la C6te Est de l'Am6rique du Nord,
par M. MacDermott, 8vo. Pam, 1864
La Loi des Temp^tes, par H. W.
Dove, 8vo. Paris, 1864
Madagascar, Cote Orientale, par
M. Germain, 8vo. Paris, 1864
Manuel de la Navigation dans la
Mer des Antilles et dans le Golfe de Mexique, 3™® Partie,
par C. P. De Kerhallet, 8vo. Paris, 1864
Mer du Nord, iv. Partie, par
A. Le Gras, 8vo. Paris, 1864
Digiti
zed by Google
Presents received during the Session 1865-66. 383
Depot G^n^ral de la Marine, Mer de Chine, i" Partie ; In- Le D6p6t Gen.
structions Nautiques, par M. A. Le Gras; Supplement, de la Marine.
par M. Costa, 8vo. Paris, 1865
La Pilote de la Nouvelle Ze-
lande; tradait de 1' Anglais, par A. Jouan, i^ et 2^
Parties. Pom, 1865
Pilote du Golfe Saint Laurent,
par Amiral H. W. Bayfield ; Traduction par A. MacDer-
mott, 8vo. Paris, 1865
Renseignements sur la Navigation
des C6tes et des Rivieres de la Gujane Fran^aise, par E. M.
Couy, 8vo. PariSy 1 865
Renseignements sur quelques
Mouillages de la C6te d'Islande et de Norv^ge, par M.
Thoyon, 8vo. Paris, 1865
Pilote de la Mer Noir, traduit
du Russe, par A. De la Planche, Cote d'Asie.
Paris, 1865
Rentier de la Cote Nord d'Es-
pagne, par A. Le Gras, 8vo. Paris, 1 864
Routier de File Aurigny, &c.,
traduit de TAnglais, par M. Jules Yavin, 8vo.
Paris, 1 865
Supplement au Routier de TAus-
tralie, tome 2"% 8vo. Paris, 1865
Dublin International Exhibition, 1865. Kingdom of Italy, Of- ^ojal Italian
ficial Catalogue, 8vo. Turin, 1 865
Edinburgh, Royal Society, Transactions, vol. xxiv., part i., The Society.
4 to. Edinburgh, 1865
Proceedings, 1864-65, 8vo.
Edinburgh, 1865
Emmens, S. H., Selections from Locke's Essay on the Human The Author.
Undertitauding, with Introduction and Notes, 8vo.
London^ 1866
Digiti
zed by Google
384 Appendix XVIL
The Society, (reneva Society of Physics, M^moires, tome xviii., i*^ partie,
4to. Geneve^ 1865
The Author, Glaisher, James, An Account of Meteorological and Physical
Observations made in five Balloon Ascents in 1863, in
continuation of eight made in the preceding year, 8yo.
Landofiy 1865
Prof. Grant. Glasgow University, Report of the Professor of Astronomy,
8vo. GUiagoWy 1866
J. R. Hind, Godward, W., Jun., Auxiliary Tables for Computing an Ap-
S>9* proximate Ephemeris of a Minor Planet, where the Angle
of Excentricity does not exceed 20 Degrees, 4to.
London^ 1866
The Society. Gottingen Boyal Society, Nachrichten, 1864, 8vo.
Gottingeny 1865
■ I Gelehrte Anzeigen, 1 864, vols. i. ii., 8vo.
Gottingen, 1865
The Author. Gray, Peter, Tables for the Formation of Logarithms and
Antilogarithms to twelve places, with Explanatory Intro-
duction, 8vo. London, 1865
Haggard, W. D., Some Comments on Portions of the " Life of
Abraham Newland," and Remarks on our present Mo-
netary System, 8vo. JVestminstery 1866
" ' " Hankel, W. G., Elektrische Untersuchungen, No. 4, 8vo.
Leipsigy 1865
^..^.^^^ Hansen, P. A., Darlegung der theoretischen Berechriung der
in den Mondtafeln angewandten Storungen, Zweite Ab-
handlung, 8vo. Leipsig, 1865
■ — . Geodatische Untersuchungen, 8vo.
Leipsig, 1865
Relationen einestheils zwischen Summen und
Dififerenzen und anderntheils zwischen Integralen und
Differentialen, 8vo. Leipsig, 1865
Harrison, R., Catalogue to the London Library, St. James's
Square, 8vo. Londony 1865
Digiti
zed by Google
Presents received during the Session 1865-66. 385
Harvard College, Report of the Committee of Overseers for TheObserva-
1 864, 8vo. Boston ( U. S.\ 1 865 ^"^qI^^^"^
Hersehel, A., Stars in the Constellations of Bode visiUe in A. Henchel,
Latitude of Greenwich, adas. ^'
Hertsprung, S., Reduction af Maskelyne's lagttagelser af The Author,
sniaa Sterner anstillede i aarene fra 1765 til 1787, 4to.
Copenhageny 1865
Hough, W. 6., Description of an Automatic Registering and —
Printing Barometer, 8vo. Albany y \%6$
Journals, The American Journal of Science and Art, Nos. 1 1 8 The Editors,
to 122, 8vo. Newhaven (IT. S.), 1865
Royal Asiatic Society, Bombay Branch, Journal, The Society.
No. 22, 8vo. Bombay^ 1865
Journal, n. s., vol. i., pt. 2,
to vol. ii., pt. I, 8vo. London^ 1865
The Assurance Magazine, Nos. 60 to 63, 8vo. Institate of
London, 1865-66 ^*^"'^"*^«-
General Index to first ten volumes, 8vo.
London, 1864
Astronomische Nachrichten, Nos. 1531 to 1586, 4to. Dr. Peters.
AUona, 1865-66
The Astronomical Register, Nos. 30 to 42, 8vo. S.Gorton, Esq.
London, 1865-66
The Athenasum Journal, Nos. 1963 to 2014, 4to. xhe Editors.
London, 1865-66
The Canadian Journal, Nos. 57 to 61, 8vo. The Canadian
Toronto, 1865-66 I^t«*«-
Cosmos, v.n., for 1865-66, 8vo. Paris, 1865-66 The Editor.
Dublin Royal Society, Journal, No. 34, 8vo. The Society.
Dtiblin, 1866
Franklin Institute, Journal, Nos. 473 to 483, 8vo. The Institute.
Philadelphia, 1865-66
Digiti
zed by Google
386
Appendix XVIL
The Royal Journals. Greographical Society (The Rojal), Journal, vol.
Oe^npUcal :^j^^{,r., 8to. London, 1865
_^ ■ ■ _^_ Proceedings,
vol, ix., No. 3, to vol. X., No. 3, 8vo. London, 1 865-66
— Geological Society, Quarterly Journal, Nos. 83 to 86,
8vo. London, 1865-66
— Herapath's Railway Journal, Nos. 1357 to 1408, 4to.
London, 1865-66
— The Horological Journal, Nos. 83 to 94, 8vo.
London, 1865-66
— The Intellectual Observer, Nos. 42 to 53, 8vo.
London, 1865-66
— The Ladies' Diary, 1724, 27, 30, 33, 34, 38, 39, 99,
London, v. y.
The Geological -
Society.
J. Herapath,
Esq.
The
Horological
Inatitate.
The Editor.
S. M. Drach,
Esq.
The Society.
The Editor.
M. I'Abb^
Moigno.
The Editor.
Dr. Francis.
The Photo-
graphicSociety.
The Editor.
The Royal
Institution.
The R. United.
Service Insti-
tution.
The Society of
Arts.
8vo.
— Linnean Society, Journal of Proceedings, vol. viii.,
Nos. 31,32. London, 1 864
The London Review, Nos. 258 to 309, folio.
London, 1865-66
— Les Mondes, v. n., 8vo. Paris, 1 865
Le Moniteur Scientifique, Nos. 203 to 226, 8vo.
Paris, 1865-66
The Philosophical Magazine, Nos. 200 to 212, 8vo.
London, 1865-66
The Photographic Journal, Nos. 155 to 169, 8vo.
London, 1865-66
The Quarterly Journal of Science, Nos. 7 to 10, 8vo.
London, 1865-66
The Reader, Nos. 128 to 175, folio. London, 1865
— Royal Institution, Journal, Nos. 41 to 43, 8vo.
London, 1865-66
— Royal United Service Institution, Journal, Nos. 34
to 38, 8vo. London, 1865-66
— Society of Ai-ts, Journal, Nos. 655 to 706, 8vo.
London, 1865-66
Digiti
zed by Google
Presents received during the Session 1865-66. 3^7 .
Karlinski, F. M., Hestice Planetee Minoris 46, Elementa Nova, The Author.
4to. CracoviiB, 1865
Krueger, A., Der Sternhanfen h Persei Beobachtungen des- '
selben am Bonner Heliometer nebst diren Berechnung,
4to. Helsingfors^ 1865
Lancashire Historic Society, Transactions, N.S., 18^4, 8vo. The Lancashire
Liverpool, 1865 g^^Jl*'
Leeds Philosophical and Literary Society. Annual Report, The Society.
1864-65, 8vo. Leeds, 1865
Leipsig Society, Berichte uber die Verhandlungen der K. Sach« The Society,
sischen Gesellschaft der Wissenschaften, 1 864, 8vo.
Leipsig, i86j;
Liebig, J. von, Induction und Deduction, 8vo. MUnchen, 1865 The Author.
Linsser, Carl, Vier von de L'Isle beobachtete Plejaden-Bedec-
kungen bearbeitet und mit Hansen's Mond-Tafeln vergli-
chen, 4to. St Petersburg, 1 864
Littrow, Karl von, Ueber eine Modification des Hansenischen _
Register Apparatus, 8vo. Vienna, i860
Liverpool, Report of the Astronomer to the Marine Committee, j. Hartnup,
Mersey Docks, &c. 1865, 8vo. Liverpool, 1866 Esq.
Literary and Philosophical Society, Proceedings, xhe Society.
No. 19, 8vo. Liverpool, 1866
Lombardy, Royal Institute. Memorie, vol. x. fasc. i. 4to. The Institute.
Milano, 1865
Rendiconto, vol. i., f. 9, 10, vol. ii.
f. I. 2. 8vo. Milano, 1864-5
Madrid, Royal Academy of Sciences, Memorias, t. vi., 4to. ' The Madrid
Madrid, xSe^-S .^^1
Academy,
Resumen de las Actas, 4to.
Madrid^ 1864
• Libros del Saber de As-
tronomia del rey D. Alfonso Rey De Castilla, t. iii. folio.
Madrid, 1864
Digiti
zed by Google
388 Appendix XVIL
TheObMrrm- Madrid Royal Obeenraiorj, Anuario, 1865, 8vo.
*^^- Madrid, 1865
, BesumeD de las Observationes
Meteorologicas hechas en el Beal ObBervatorio de Madrid
durante el Afio del mismo nombre 1 863, 4to.
Mcidridy 1864
The Libnrj. Manchester Free Library, Catalogue of the Books, Reference
Department, 8vo. Londotiy 1864
The Author. Marth, A., Auxiliary Tables for the Solution of Lambert's
Equation, with a few Remarks on the Determination of
Cometary Orbits, 4to. London, 1865
(M'Clintock, Miss), A New Theory of Astronomy, derived from
the latest discoveries, izmo. Dublin, 1857
The Society. Meteorological Society, The British, Proceedings, Nos. 20 to
24, 8vo. London, 1865-66
The Author. Mittenius, G., Ueber die Hymenophyllaceae, Nq. 2, 8vo.
Leipsig, 1864
The Academy. Munich Royal Academy, Sitzungsberichte, 1865, ii. heft. 3, 4,
8vo. Miinchen, 1 865
The Author. Nageli, Carl, Enstehung und Begriff der Naturhistorischen Art.
Zweite auflage, 8vo. Miinchen, 1 865
- Nagy, K., Die Sonne und die Astronomic, 8vo. Leipsig, 1 866
The Naples Naples, Royal Society, Rendiconto, July 1 860, 4to.
Royal Society. Naples, 1 864
The Lords The Nautical Almanac for 1 869, and Supplement, 8vo.
^^Tme'''''^* ^ndon, 1865
Admiralty.
The Author. Oudemans, J. A., Herlieding van de Waamemingen gedaan
door de Heeren S. H. en G. A. de Lange ter Bepaling
van de Lengte van Menado, Kema, Boeton, Tern ate en
Makasar in de Jaren 1852 en 1853, 8vo. Batavia, n,d.
— ', Hernieuwde Bepaling van de Lengte van
Batavia, 8vo. Batavia, n.d.
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Presents received during the Session 1865-66. 389
Oudemans^ J. A«, Yerslag van de Dienstreiasen, 8vo. The Author*
Batavia, 1864
, Verslag van de Deinstreis van den Hoofd-
ingenieur van de Greographische Dienst^ in JuUi en Au-
gustas 1863, 8vo. BataviUy 1864
-, Vervolg op het Verslag van de Bepaling '
der Geographische Ligging van dei Haatzen op Java
waar Telegraafkantoren gevestigd zijn, Svo.
Batavia^ n.d,
Palermo, BuUetino Meteorologico del R. Osservatorio, vol. i. The Obaenra-
No. 5 to vol. ii. No. i, fol. Palermo, 1865 y^^^o,
Royal Institute, Giornale de Scienze Naturali ed The Institute.
Economiche, vol. i. f. i, 2. fol. Palermo, 1865
Parallax (Rowbotliam) Zetetic Astronomy: Earth not a Globe. Mr. J .Williams.
An Experimental Inquiry into the True Figure of the
Earth, proving it a Plane without axial or orbital mo-
tion, and the only material World in the Universe, 1 2mo.
London^ 1865
Pieter Maritzburg, Meteorological Observations in 1 864, folio. Dr. Mann.
Pieter Maritzburg, 1865
Plantamour, E., Recherches sur la Distribution de la Tempera- The Author.
ture ^ la Surface de la Suisse pendant I'Hiver, 1863-4,
8vo. Geneve, 1 865
Resum6 M^t^orologique de TAnn^e 1864, pour
Geneve et le Grand St. Bernard, 8vo. Geneve, 1 865
Petersbourg, St., Academic Imperial des Sciences, Bulletins, The Academy.
t. vii., viii., folio. St. Petersbourg, 1 865
■ Melanges Math^mati- The Authors.
ques et Astronomiques :
1 . Observations du Satellite de Sirius, par 0. Struve.
2. Observations de quelques Nebuleuses, „
3. Neue Berechnung der Sirius Parallaxe, von H.
Gylden.
4. Uber den Gang der Pulkowaer Normalurh, von A.
Wagner, 8vo, St Petersburg, 1 864
Digiti
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390 Appendix XVIL
The Observa- Poulkowa Observatory, Jahresbericht am 1 7 Mai 1 864 dem
^^^' Comite der Nicolai Haupsternwarte abgestattet vom Di-
rector der Stern warte, 8vo. St. Petersburg, 1 864^
The Author. Pratt, John H., Archdeacon of Calcutta, A Treatise on At-
tractions : La Place's Functions and the Figure of the
Earth, 8vo. London, 1865
^ Proctor, B. A., The Stars, in Twelve Maps on the Gnomonic
Projection, ob. folio. London, 1 866
Quetelet, A., Histoire des Sciences Math^matiques et Physiques
chez les Beiges, 8vo. Brussels, 1864
TheRadcliffe Radcliffe Observatory, Astronomical and Meteorological Ob-
Trustees, servations in the year 1863, 8vo. Oxford, 1866
The Academy. Royal Irish Academy, Transactions, 6 parts of vol. xxiv. 4to.
Dublin, 1864-5
J Proceedings, vol. viii., vol. ix. pt. i, 8vo.
Dublin, 1864-5
The Society. Royal Scottish Society of Arts, Transactions, vol. vii., part i.,
8vo. Edinburgh, 1865
Royal Society, Philosophical Transactions, vol. cliv., part 3 5
civ., parts I and 2, 4to. London, 1865
' Proceedings, Nos. 75 to 83, 8vo.
London, 1865
The Author. Ryan, Matthew, The celebrated Theory of Parallels : Demon-
stration of the celebrated Theorem, Euclid i, axiom 12,
8vo. Washington, 1866
The Observa- San Fernando Observatory, Almanaque Nautico para 1867.
tory.
The Author, Santini, Giov., Relazione intorno alle Attrazioni locali resul-
tanti nei contorni di Mosca, 4to. Venice, 1 865
Schonfield, E., Catalog von Yeranderlichen Sternen mit Ein-
schluss der Neuen Sternen, 8vo. Manheim, 1 865
The Institution. Smithsonian Institution, Contributions to Knowledge, vol. xiv.,
4to. Washington', 1865
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Presents received during the Session 1 865-66. 39 r
Smithsonian Institution, Annaal Report of Board of Regents, The Institution,
for 1863, 8vo. Washingtony 1864
, Results of Meteorological Observa- — —
tion from 1854 to 1859, vol.ii. pt. i, 4to.
Washington^ 1864
Stanley, W. F., A Descriptive Treatise on Mathematical Draw- The Author,
ing Instruments, 8vo. London^ 1 866
Stockholm Royal Academy, Handlingar, ny Foljd, Femte The Academy.
Bandet, Forsten Haftet, 1863, 4to. Stockholm, 1864
, Oversigt, Forhandlingar, 1864,
8vo. Stockholm^ 181 5
Stonyhurst College Observatory, Results of the Meteorological The College. -
and Magnetical Observations, 1865, 8vo. ClitheroCy i%66
Strong, C. D., Sanctse Vigiliae, or Devout Musings on the S.M. Drach,
Heavens, in' verse, i zmo. London, 1 844 ^*^*
Sydney, Government Observatory, Report of Astronomer for G. R. Smalley,
1864, folio. Sydney, i%6s ^'^'
Tasmania Royal Society, Reports for 1863, 1864, 8vo. The Royal
HobartTown,i%6^-S ^^^^_
, Monthly Notices for 1863-4, ^^^'
Hohart Town, 1863-4
, Abstracts of Meteorological Obser-
vations made in Tasmania during the six months ending
June 1864, sheet. 1864
Tornamiri, F. V. de, Chronographia y Repertorio de los Tiem- j. Bucking-
pos a lo Modemo, el qual trata varias y diversas cosas de ^™' ^^'
Cosmographia, Sphera, Theorica de Planttas, Philosophic,
&c. 4to. Pampeluna, 1585
Turin Royal Academy, Memorie, serie z****. t. xxi. 4to. The Academy.
Torino, 1865
^ Atti, 1865-6, 8vo. Torino, 1866
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39* Appendix XVIL
inie AmericMi United States, The American Ephemeris and Nautical AI-
manac for 1866, 8vo. Washington, 1864
Asteroids for 1 865 ; Supplement to American
Ephemeris for 1866, 8vo. Washington, 1864
, Almanac Catalogue of Zodiacal Stars, 8vo.
Washington, 1864
Tables of Mercury for the use of the American
Ephemeris by Jos. Winlock, 4to. Washington, 1 864
Statistics of Foreign and Domestic Commerce
of the United States, 8yo. Washington, 1864
Dr. Bache. , Report of the Superintendent of the Coast
Survey during 1 862, 4to. Washington, 1 864
The Society. Upsala Boyal Society, Nova Acta, vol. ii. 4to. UpsaluB, 1 864
, Universitats Arsskrift, 1864, 8vo. Upsala, 1864
The Society. Victoria Royal Society, Transactions and Proceedings, vol. vi.
8vo. Melbourne, I S6^
The Academy. Vienna Imperial Academy of Science, Denkschriften, Band
xxiv., 4to. Vienna, 1865
Sitzungsberichte, 1864, Band 51,
52, 53, 1865, 8vo. JFienna, 1865
The Austrian Vienna, Reise der Osterreichischen Fregate Novara am die
Erde in den Jahren 1857, 1858, 1859, Nautisch Physica-
lischer Theil iii. Abtheilung Meteorologisches Tagebuch,
4to. Vienna, 1865
The Author. Wackerbarth, A. F. D., Om. Planeten Neptunus, 8vo.
Upsala, 1865
__ , A Provisional Theory of Leda, 4to.
Upsala, 1866
^ Wilcocks, Alex., Thoughts on the Influence of Ether in the
Solar System, its relation to the Zodiacal Light, Cometo,
the Seasons, and periodical Shooting- Stars, 4to.
Philadelphia, 1864
Digiti
zed by Google
Presents received during the Session 1865-66. 393
Winnecke, A., Pulkowaer Beobachtungen des hellen Cometen The Author,
von 1 862, nebst einigen Bemerkungen, 4to.
St, Petersburg, 1864
Wolf, C, Recherches sur I'Equation personelle dans lea Obser-
vations des passages, sa determination absolue, ses lois et son
origine, 4to. Paris, 1866
Wolf, Rudolf, Mittheilungen iiber die Sonnenflecken, No. 18
et 21, 8to. Zurich, 1865
Zoller, J. C. F., Theorie der Relatiyen Licbtstarke der Mond-
phaseuy 8yo. Leipsig, 1865
— — , Pbotometriscbe untersucbungen mit beson- ::.
derer Racksiebt auf die pbjsiscbe Bescbaffenbeit der bim-
melsKorper, 8yo. Leipsig, 1865
Miscellaneous.
Le Depdt
Forty-Fiye Cbarts. General de da
Marine.
A Diagram sbowing tbe Times of Sunrise and Sunset, also tbe The Author.
Duration of Twiligbt and the Equation of Time for every
day in tbe year in tbe Latitude of London, viz, 51°' 30 N,
by Charles Ansell. Sheet.
Four Stereoscopic Slides of the Moon. Josh Beck,
^ Esq.
Digiti
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394 Appendix XVIL
Books, SfC, purchased with the Tumor Fund.
Delaunay, C, Cours El^mentaire d'ulstronomie, 8vo.
Parisy 1865
Guillemin, Am6d^, La Lune, 8 vo. Parisy 1 866
Kepler, Joh., Opera Omnia, vol. vi., part i, 8vo.
Frankfurtij 1865
Kirby, Joshua, Dr. Brook Taylor's Method of Perspective
made Easy, both in Theory and Practice, with an Atlas of
Plates, 4to. London^ 1768
Lias, Emnd., L'Espace Celeste et La Nature Tropicale, 8vo.
PariSj 1866
Madler, J. H., Der Wunderbau des Weltals, oder Populaire
Astronomic, with an Atlas of Plates, 8vo. Berlin^ 1861
Schroeter, J. H., Seleno-topographische Fragmente zur-gen-
auern Kenntniss der Mondflache ihrer erlettenen Yeran-
derungen und Atmosphare sammt den dazu gehorigen
specialcharten und zerechnungen, 2 vols. 4to.
Crottingen, 179 1-1802
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